The present study aims to consider a mathematical eco-epidemiological model involving two fractio... more The present study aims to consider a mathematical eco-epidemiological model involving two fractional operators. To this end, we provide approximate solutions to these fractional systems through the application of a numerical technique that is based on the rule of product integration. This feature contributes greatly to the efficiency and effectiveness of both methods. We have also presented some theoretical discussions related to the equilibrium points of the system. Further, several numerical simulations are presented in order to illustrate the impact of choosing different parameters on the dynamics of the model. It is demonstrated that the obtained numerical results are completely consistent with the expected theoretical results. Moreover, both techniques can be used to solve other problems in epidemiology and describe other problems in the future. The article's model has never been studied via the employed fractional operators, and this is a distinct point for our work and ot...
This article presents a new three-step implicit iterative method. The proposed method is used to ... more This article presents a new three-step implicit iterative method. The proposed method is used to approximate the fixed points of a certain class of pseudocontractive-type operators. Additionally, the strong convergence results of the new iterative procedure are derived. Some examples are constructed to authenticate the assumptions in our main result. At the end, we use our new method to solve a fractional delay differential equation in the sense of Caputo. Our main results improve and generalize the results of many prominent authors in the existing literature.
This paper introduces some numerical algorithms for finding solutions of nonlinear problems like ... more This paper introduces some numerical algorithms for finding solutions of nonlinear problems like functional equations, split feasibility problems (SFPs) and variational inequality problems (VIPs) in the setting of Hilbert and Banach spaces. Our approach is based on the Thakur-Thakur-Postolache (TTP) iterative algorithm and the class of mean nonexpansive mappings. First we provide some convergence results (including weak and strong convergence) in the setting of Banach space. To support these results, we provide a numerical example and prove that our TTP algorithm in this case converges faster to fixed point compared to other iterative algorithms of the literature. After that, we consider two new TTP type projection iterative algorithms to solve SFPs and VIPs on the Hilbert space setting. Our result are new in analysis and suggest new type effective numerical algorithms for finding approximate solutions of some nonlinear problems.
In this manuscript, owing to the concept of bicomplex b-metric spaces, we prove common fixed poin... more In this manuscript, owing to the concept of bicomplex b-metric spaces, we prove common fixed point theorem in bicomplex b-metric spaces. In order to strengthen our main results, a suitable example is presented. More over, the results we obtained is supplement and improve on previous research findings. A fruitful application is also supplied to endorse our outcomes
Entropy is essential. Entropy is a measure of a system’s molecular disorder or unpredictability, ... more Entropy is essential. Entropy is a measure of a system’s molecular disorder or unpredictability, since work is produced by organized molecular motion. Entropy theory offers a profound understanding of the direction of spontaneous change for many commonplace events. A formal definition of a random graph exists. It deals with relational data’s probabilistic and structural properties. The lower-order distribution of an ensemble of attributed graphs may be used to describe the ensemble by considering it to be the results of a random graph. Shannon’s entropy metric is applied to represent a random graph’s variability. A structural or physicochemical characteristic of a molecule or component of a molecule is known as a molecular descriptor. A mathematical correlation between a chemical’s quantitative molecular descriptors and its toxicological endpoint is known as a QSAR model for predictive toxicology. Numerous physicochemical, toxicological, and pharmacological characteristics of chemic...
As it is not always true that the distance between the points in fuzzy rectangular metric spaces ... more As it is not always true that the distance between the points in fuzzy rectangular metric spaces is one, so we introduce the notions of rectangular and b-rectangular metric-like spaces in fuzzy set theory that generalize many existing results, which can be regarded as the main advantage of this paper. In these spaces, the symmetry property is preserved, but the self distance may not be equal to one. We discuss topological properties and demonstrate that neither of these spaces is Hausdorff. Using α−ψ-contraction and Geraghty contractions, respectively, in our main results, we establish fixed point results in these spaces. We present examples that justify our definitions and results. We use our main results to demonstrate that the solution of a nonlinear fractional differential equation for HIV is unique.
In this paper, we explore some extensions of multiple fixed point results for various distance sp... more In this paper, we explore some extensions of multiple fixed point results for various distance spaces such as s-distance space, s,q-distance space, and balanced distance space. Some examples are also discussed for the elaboration of these generalized structures. An application of our result that demonstrates the existence of a unique solution of a system of integral equations is also provided.
We discuss a pair of nonlinear matrix equations (NMEs) of the form X=R1+∑i=1kAi*F(X)Ai, X=R2+∑i=1... more We discuss a pair of nonlinear matrix equations (NMEs) of the form X=R1+∑i=1kAi*F(X)Ai, X=R2+∑i=1kBi*G(X)Bi, where R1,R2∈P(n), Ai,Bi∈M(n), i=1,⋯,k, and the operators F,G:P(n)→P(n) are continuous in the trace norm. We go through the necessary criteria for a common positive definite solution of the given NME to exist. We develop the concept of a joint Suzuki-implicit type pair of mappings to meet the requirement and achieve certain existence findings under weaker assumptions. Some concrete instances are provided to show the validity of our findings. An example is provided that contains a randomly generated matrix as well as convergence and error analysis. Furthermore, we offer graphical representations of average CPU time analysis for various initializations.
A generalised common fixed point theorem of Tasković type for three mappings f : X → X and S, T :... more A generalised common fixed point theorem of Tasković type for three mappings f : X → X and S, T : X k → X in a cone b-metric space is proved. Our result generalises many well-known results. 2010 Mathematics Subject Classification. 47H10.
In this manuscript, we present further extensions of the best approximation theorem in hyperconve... more In this manuscript, we present further extensions of the best approximation theorem in hyperconvex spaces obtained by Khamsi.
New families of uniformities are introduced on UC(X,Y) , the class of uniformly continuous mappin... more New families of uniformities are introduced on UC(X,Y) , the class of uniformly continuous mappings between X and Y, where (X,{\mathcal{U}}) and (Y,{\mathcal{V}}) are uniform spaces. Admissibility and splittingness are introduced and investigated for such uniformities. Net theory is developed to provide characterizations of admissibility and splittingness of these spaces. It is shown that the point-entourage uniform space is splitting while the entourage-entourage uniform space is admissible.
In the present paper, we established multivalued fixed point results on C*-algebra valued metric ... more In the present paper, we established multivalued fixed point results on C*-algebra valued metric spaces and utilized the same to prove fixed point results via Suzuki type contraction. An example is also given to exhibit the utility of our main result. We also provided a system of Fredholm integral equations to examine the existence and uniqueness of solutions supporting our main result.
In this paper we introduce dislocated and dislocated quasi version of a cone b-metric space over ... more In this paper we introduce dislocated and dislocated quasi version of a cone b-metric space over a Banach algebra as well as weak semi α-admissible and α-identical pair of mappings and prove common fixed point theorems for a pair of α-identical and weak α-admissible mappings in the aforesaid spaces. Our results are supported with suitable examples and an application to a system of m-tupled functional equations.
We have introduced the new notions of R-weakly graph preserving and R-weakly α -admissible pair o... more We have introduced the new notions of R-weakly graph preserving and R-weakly α -admissible pair of multivalued mappings which includes the class of graph preserving mappings, weak graph preserving mappings as well as α -admissible mappings of type S, α * -admissible mappings of type S and α * - orbital admissible mappings of type S respectively. Some generalized contraction and rational contraction classes are also introduced for a pair of multivalued mappings and common fixed point theorems are proved in a b-metric space endowed with a graph. We have also applied our results to obtain common fixed point theorems for R-weakly α -admissible pair of multivalued mappings in a b-metric space which are the proper extension and generalization of many known results. Proper examples are provided in support of our results. Our main results and its consequences improve, generalize and extend many known fixed point results existing in literature.
A dislocated cone metric space over Banach algebra is introduced as a generalisation of a cone me... more A dislocated cone metric space over Banach algebra is introduced as a generalisation of a cone metric space over Banach algebra as well as a dislocated metric space. Fixed point theorems for Perov-type α-quasi contraction mapping, Kannan-type contraction as well as Chatterjee-type contraction mappings are proved in a dislocated cone metric space over Banach algebra. Proper examples are provided to establish the validity of our claims.
In this paper, we introduce the ( C , Ψ * , G ) class of contraction mappings using C-class funct... more In this paper, we introduce the ( C , Ψ * , G ) class of contraction mappings using C-class functions and some improved control functions for a pair of set valued mappings as well as a pair of single-valued mappings, and prove common fixed point theorems for such mappings in a metric space endowed with a graph. Our results unify and generalize many important fixed point results existing in literature. As an application of our main result, we have derived fixed point theorems for a pair of α -admissible set valued mappings in a metric space.
Journal of Nonlinear Sciences and Applications, 2015
The concept of rectangular b-metric space is introduced as a generalization of metric space, rect... more The concept of rectangular b-metric space is introduced as a generalization of metric space, rectangular metric space and b-metric space. An analogue of Banach contraction principle and Kannan's fixed point theorem is proved in this space. Our result generalizes many known results in fixed point theory.
The concept of Horizontallly Weak Compatibility of mappings is introduced and common fixed point ... more The concept of Horizontallly Weak Compatibility of mappings is introduced and common fixed point theorems for two pairs of mappings are proved in dislocated fuzzy metric space using horizontally weak compatibility condition. Our results extends and generalises many existing fixed point theorems. Reny George et al.
The purpose of this paper is to obtain common fixed point theorems for compatible maps of type (A... more The purpose of this paper is to obtain common fixed point theorems for compatible maps of type (A-I) and type (A2) on fuzzy metric spaces. Our results extend, generalize and fuzzify several fixed point theorems on metric paces, menger probabilistic metric spaces, uniform spaces and fuzzy metric spaces.
International Journal of Mathematical Analysis, 2014
Common fixed point theorems for two pairs of mappings are proved in dislocated fuzzy metric space... more Common fixed point theorems for two pairs of mappings are proved in dislocated fuzzy metric space using horizontally weak compatibility condition. Our results extends and generalises many existing fixed point theorems.
The present study aims to consider a mathematical eco-epidemiological model involving two fractio... more The present study aims to consider a mathematical eco-epidemiological model involving two fractional operators. To this end, we provide approximate solutions to these fractional systems through the application of a numerical technique that is based on the rule of product integration. This feature contributes greatly to the efficiency and effectiveness of both methods. We have also presented some theoretical discussions related to the equilibrium points of the system. Further, several numerical simulations are presented in order to illustrate the impact of choosing different parameters on the dynamics of the model. It is demonstrated that the obtained numerical results are completely consistent with the expected theoretical results. Moreover, both techniques can be used to solve other problems in epidemiology and describe other problems in the future. The article's model has never been studied via the employed fractional operators, and this is a distinct point for our work and ot...
This article presents a new three-step implicit iterative method. The proposed method is used to ... more This article presents a new three-step implicit iterative method. The proposed method is used to approximate the fixed points of a certain class of pseudocontractive-type operators. Additionally, the strong convergence results of the new iterative procedure are derived. Some examples are constructed to authenticate the assumptions in our main result. At the end, we use our new method to solve a fractional delay differential equation in the sense of Caputo. Our main results improve and generalize the results of many prominent authors in the existing literature.
This paper introduces some numerical algorithms for finding solutions of nonlinear problems like ... more This paper introduces some numerical algorithms for finding solutions of nonlinear problems like functional equations, split feasibility problems (SFPs) and variational inequality problems (VIPs) in the setting of Hilbert and Banach spaces. Our approach is based on the Thakur-Thakur-Postolache (TTP) iterative algorithm and the class of mean nonexpansive mappings. First we provide some convergence results (including weak and strong convergence) in the setting of Banach space. To support these results, we provide a numerical example and prove that our TTP algorithm in this case converges faster to fixed point compared to other iterative algorithms of the literature. After that, we consider two new TTP type projection iterative algorithms to solve SFPs and VIPs on the Hilbert space setting. Our result are new in analysis and suggest new type effective numerical algorithms for finding approximate solutions of some nonlinear problems.
In this manuscript, owing to the concept of bicomplex b-metric spaces, we prove common fixed poin... more In this manuscript, owing to the concept of bicomplex b-metric spaces, we prove common fixed point theorem in bicomplex b-metric spaces. In order to strengthen our main results, a suitable example is presented. More over, the results we obtained is supplement and improve on previous research findings. A fruitful application is also supplied to endorse our outcomes
Entropy is essential. Entropy is a measure of a system’s molecular disorder or unpredictability, ... more Entropy is essential. Entropy is a measure of a system’s molecular disorder or unpredictability, since work is produced by organized molecular motion. Entropy theory offers a profound understanding of the direction of spontaneous change for many commonplace events. A formal definition of a random graph exists. It deals with relational data’s probabilistic and structural properties. The lower-order distribution of an ensemble of attributed graphs may be used to describe the ensemble by considering it to be the results of a random graph. Shannon’s entropy metric is applied to represent a random graph’s variability. A structural or physicochemical characteristic of a molecule or component of a molecule is known as a molecular descriptor. A mathematical correlation between a chemical’s quantitative molecular descriptors and its toxicological endpoint is known as a QSAR model for predictive toxicology. Numerous physicochemical, toxicological, and pharmacological characteristics of chemic...
As it is not always true that the distance between the points in fuzzy rectangular metric spaces ... more As it is not always true that the distance between the points in fuzzy rectangular metric spaces is one, so we introduce the notions of rectangular and b-rectangular metric-like spaces in fuzzy set theory that generalize many existing results, which can be regarded as the main advantage of this paper. In these spaces, the symmetry property is preserved, but the self distance may not be equal to one. We discuss topological properties and demonstrate that neither of these spaces is Hausdorff. Using α−ψ-contraction and Geraghty contractions, respectively, in our main results, we establish fixed point results in these spaces. We present examples that justify our definitions and results. We use our main results to demonstrate that the solution of a nonlinear fractional differential equation for HIV is unique.
In this paper, we explore some extensions of multiple fixed point results for various distance sp... more In this paper, we explore some extensions of multiple fixed point results for various distance spaces such as s-distance space, s,q-distance space, and balanced distance space. Some examples are also discussed for the elaboration of these generalized structures. An application of our result that demonstrates the existence of a unique solution of a system of integral equations is also provided.
We discuss a pair of nonlinear matrix equations (NMEs) of the form X=R1+∑i=1kAi*F(X)Ai, X=R2+∑i=1... more We discuss a pair of nonlinear matrix equations (NMEs) of the form X=R1+∑i=1kAi*F(X)Ai, X=R2+∑i=1kBi*G(X)Bi, where R1,R2∈P(n), Ai,Bi∈M(n), i=1,⋯,k, and the operators F,G:P(n)→P(n) are continuous in the trace norm. We go through the necessary criteria for a common positive definite solution of the given NME to exist. We develop the concept of a joint Suzuki-implicit type pair of mappings to meet the requirement and achieve certain existence findings under weaker assumptions. Some concrete instances are provided to show the validity of our findings. An example is provided that contains a randomly generated matrix as well as convergence and error analysis. Furthermore, we offer graphical representations of average CPU time analysis for various initializations.
A generalised common fixed point theorem of Tasković type for three mappings f : X → X and S, T :... more A generalised common fixed point theorem of Tasković type for three mappings f : X → X and S, T : X k → X in a cone b-metric space is proved. Our result generalises many well-known results. 2010 Mathematics Subject Classification. 47H10.
In this manuscript, we present further extensions of the best approximation theorem in hyperconve... more In this manuscript, we present further extensions of the best approximation theorem in hyperconvex spaces obtained by Khamsi.
New families of uniformities are introduced on UC(X,Y) , the class of uniformly continuous mappin... more New families of uniformities are introduced on UC(X,Y) , the class of uniformly continuous mappings between X and Y, where (X,{\mathcal{U}}) and (Y,{\mathcal{V}}) are uniform spaces. Admissibility and splittingness are introduced and investigated for such uniformities. Net theory is developed to provide characterizations of admissibility and splittingness of these spaces. It is shown that the point-entourage uniform space is splitting while the entourage-entourage uniform space is admissible.
In the present paper, we established multivalued fixed point results on C*-algebra valued metric ... more In the present paper, we established multivalued fixed point results on C*-algebra valued metric spaces and utilized the same to prove fixed point results via Suzuki type contraction. An example is also given to exhibit the utility of our main result. We also provided a system of Fredholm integral equations to examine the existence and uniqueness of solutions supporting our main result.
In this paper we introduce dislocated and dislocated quasi version of a cone b-metric space over ... more In this paper we introduce dislocated and dislocated quasi version of a cone b-metric space over a Banach algebra as well as weak semi α-admissible and α-identical pair of mappings and prove common fixed point theorems for a pair of α-identical and weak α-admissible mappings in the aforesaid spaces. Our results are supported with suitable examples and an application to a system of m-tupled functional equations.
We have introduced the new notions of R-weakly graph preserving and R-weakly α -admissible pair o... more We have introduced the new notions of R-weakly graph preserving and R-weakly α -admissible pair of multivalued mappings which includes the class of graph preserving mappings, weak graph preserving mappings as well as α -admissible mappings of type S, α * -admissible mappings of type S and α * - orbital admissible mappings of type S respectively. Some generalized contraction and rational contraction classes are also introduced for a pair of multivalued mappings and common fixed point theorems are proved in a b-metric space endowed with a graph. We have also applied our results to obtain common fixed point theorems for R-weakly α -admissible pair of multivalued mappings in a b-metric space which are the proper extension and generalization of many known results. Proper examples are provided in support of our results. Our main results and its consequences improve, generalize and extend many known fixed point results existing in literature.
A dislocated cone metric space over Banach algebra is introduced as a generalisation of a cone me... more A dislocated cone metric space over Banach algebra is introduced as a generalisation of a cone metric space over Banach algebra as well as a dislocated metric space. Fixed point theorems for Perov-type α-quasi contraction mapping, Kannan-type contraction as well as Chatterjee-type contraction mappings are proved in a dislocated cone metric space over Banach algebra. Proper examples are provided to establish the validity of our claims.
In this paper, we introduce the ( C , Ψ * , G ) class of contraction mappings using C-class funct... more In this paper, we introduce the ( C , Ψ * , G ) class of contraction mappings using C-class functions and some improved control functions for a pair of set valued mappings as well as a pair of single-valued mappings, and prove common fixed point theorems for such mappings in a metric space endowed with a graph. Our results unify and generalize many important fixed point results existing in literature. As an application of our main result, we have derived fixed point theorems for a pair of α -admissible set valued mappings in a metric space.
Journal of Nonlinear Sciences and Applications, 2015
The concept of rectangular b-metric space is introduced as a generalization of metric space, rect... more The concept of rectangular b-metric space is introduced as a generalization of metric space, rectangular metric space and b-metric space. An analogue of Banach contraction principle and Kannan's fixed point theorem is proved in this space. Our result generalizes many known results in fixed point theory.
The concept of Horizontallly Weak Compatibility of mappings is introduced and common fixed point ... more The concept of Horizontallly Weak Compatibility of mappings is introduced and common fixed point theorems for two pairs of mappings are proved in dislocated fuzzy metric space using horizontally weak compatibility condition. Our results extends and generalises many existing fixed point theorems. Reny George et al.
The purpose of this paper is to obtain common fixed point theorems for compatible maps of type (A... more The purpose of this paper is to obtain common fixed point theorems for compatible maps of type (A-I) and type (A2) on fuzzy metric spaces. Our results extend, generalize and fuzzify several fixed point theorems on metric paces, menger probabilistic metric spaces, uniform spaces and fuzzy metric spaces.
International Journal of Mathematical Analysis, 2014
Common fixed point theorems for two pairs of mappings are proved in dislocated fuzzy metric space... more Common fixed point theorems for two pairs of mappings are proved in dislocated fuzzy metric space using horizontally weak compatibility condition. Our results extends and generalises many existing fixed point theorems.
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