In (1), A. Branciari defines a Generalised metric space of finite order �# and establishes Banach... more In (1), A. Branciari defines a Generalised metric space of finite order �# and establishes Banach contraction principle in it. The object of this paper is to extend this result to Quasi contraction and prove some fixed point results for two weakly compatible self maps satisfying a generalized contractive condition in this space without assuming it to be Hausdorff . Our result generalizes the said result of (1). All the results presented in this paper are new.
Abstract. This paper introduces the notion of semi-compatible self-maps in 2-metric spaces and es... more Abstract. This paper introduces the notion of semi-compatible self-maps in 2-metric spaces and establishes a fixed point theorem for four self-maps, satisfying an implicit relation through semi-compatibility of a pair of self-maps. This results in another fixed point ...
The aim of this paper is to introduce the notion of interpolative fuzzy Z-contractive condition f... more The aim of this paper is to introduce the notion of interpolative fuzzy Z-contractive condition for a pair of self maps in a fuzzy metric space, which enlarges, unifies and generalizes the existing fuzzy contractions (by Gregori and Sapena [6]), ψ contraction (by Mihet [11]), fuzzy Z-contractions (by Shukla et al. [21]) and Tirado contraction (by Tirado [22]), which are for only one self map. Using this, we establish a unique common fixed point theorem for two self maps satisfying condition (S), which was introduced by Shukla et al. in [21] through weak compatibility. As an applications, we discuss fixed point theorem for Fredholm non-linear integral equation. The article also includes an example, which shows the validity of our results.
Introduction/purpose: The aim of this paper is to introduce the notion of an interpolative genera... more Introduction/purpose: The aim of this paper is to introduce the notion of an interpolative generalised Meir-Keeler contractive condition for a pair of self maps in a fuzzy metric space, which enlarges, unifies and generalizes the Meir-Keeler contraction which is for only one self map. Using this, we establish a unique common fixed point theorem for two self maps through weak compatibility. The article includes an example, which shows the validity of our results. Methods: Functional analysis methods with a Meir-Keeler contraction. Results: A unique fixed point for self maps in a fuzzy metric space is obtained. Conclusions: A fixed point of the self maps is obtained.
International Journal of Engineering Sciences, 2021
Graphene-enabled nano antennas constitute a novel paradigm which is a current trend of research a... more Graphene-enabled nano antennas constitute a novel paradigm which is a current trend of research among designers. Graphene-based nano-antennas with nanometer in size have shown to radiate electromagnetic waves at the terahertz (THz) frequency band. Proposed research activity is an attempt of Terahertz Nano dipole antenna design through the Finite Difference Time Domain (FDTD) based numerical simulation software, i.e. CST. Graphene material as adipole antenna has been explored to get a radiation performance. Before hand absorption, reflection and transmission characteristics of the grapheme layer has been explored. Designed antenna is analyzed in terms of the reflection coefficient, and radiation pattern etc. An attempt has been done for resonance study of graphene based nano dipole antennas, in that patch antenna length parameteris changed and performance is observed. The impact of most crucial parameter, i.e., chemical potential on the grapheme radiation performance has been analyze...
The object of this paper is to introduce the concept of compatibility of pair of self maps in a c... more The object of this paper is to introduce the concept of compatibility of pair of self maps in a cone metric space without assuming its normality. Using this concept we establish a unique common fixed point theorem for four self maps satisfying a generalized contractive ...
The object of this paper is to introduce the notion of semi-compatible maps in fuzzy metric space... more The object of this paper is to introduce the notion of semi-compatible maps in fuzzy metric spaces, fuzzy 2-metric spaces and fuzzy 3-metric spaces and to establish three common fixed point theorems for these spaces for four self-maps. These results improve, extend and generalize the results of [16]. As an application , these results have been used to obtain translation and generalization of Grabeic's contraction principle in the new settings. All the result presented in this paper are new.
Journal of Nonlinear Sciences and Applications, 2010
The object of this paper is to establish unique common fixed point theorems for four self maps sa... more The object of this paper is to establish unique common fixed point theorems for four self maps satisfying a new contractive condition in a modified intuitionistic fuzzy metric space through compatibility of type (P). A generalization of a result of D Turkoglu et al [J. Apply. Math. Computing (2006)] in the setting of a modified intuitionistic fuzzy metric space follows from them. Modified intuitionistic fuzzy version of Grabiec contraction Principle has also been established. All the results presented in this paper are new. Examples have been constructed in support of the main results of this paper.
B. Singh and R. K. Sharma [Demonstratio Math. Vol. 36, No.l (2003), 215-220] have proved two comm... more B. Singh and R. K. Sharma [Demonstratio Math. Vol. 36, No.l (2003), 215-220] have proved two common fixed point theorems for two self-maps satisfying an expansive condition in Dmetric spaces. This note offers generalization for these theorems for three self-maps using weakcompatibility and reduces the domain of ζ to an orbit only. The last theorem proves that the continuity of none of two or three maps is required in the setting of Dmetric space.
This paper deals with a general contraction. Two fixed-point theorems for a limit weak-compatible... more This paper deals with a general contraction. Two fixed-point theorems for a limit weak-compatible pair of a multi-valued map and a self map on a D-metric space have been established. These results improve significantly, the main results of Dhage, Jennifer and Kang [5] by reducing its assumption and generalizing its contraction simultaneously. At the same time some results of Singh, Jain and Jain [12] are generalized from a self map to a pair of a set-valued and a self map. Theorems of Veerapandi and Rao [16] get generalized and improved by these results. All the results of this paper are new.
The aim of this paper is to introduce fuzzy generalised weak contractive condition for a pair of ... more The aim of this paper is to introduce fuzzy generalised weak contractive condition for a pair of self maps in a fuzzy metric space,which is in accordance with the theory of metric spaces given by Rhoades (Nonlinear Analysis 47:2683–2693, 2001). Our results generalize existing fuzzy contraction (by Gregori and Sapena (Fuzzy Sets System 125:245–252, 2002), which is for only one self map. Using this, we establish a unique common fixed point theorem for two self-maps through weak compatibility. The article includes an example, in support of our results. Also an application we established, for the existence and uniqueness of a solution of Fredholm non-linear integral equation in the setting of fuzzy metric space.
The object of this paper is to establish a unique common fixed point theorem for six self-mapping... more The object of this paper is to establish a unique common fixed point theorem for six self-mappings satisfying a generalized contractive condition through compatibility of type (β) and weak compatibility in a fuzzy metric space. It significantly generalizes the result of Singh and Jain [The Journal of Fuzzy Mathematics (2006)] and Sharma [Fuzzy Sets and Systems (2002)]. An example has been constructed in support of our main result. All the results presented in this paper are new.
The aim of this paper is to introduce Zs-contractive condition for a pair of self maps in a fuzzy... more The aim of this paper is to introduce Zs-contractive condition for a pair of self maps in a fuzzy metric space, which enlarges and unifies the existing fuzzy contractions (by Gregori and Sapena [4]), ψcontraction (by Mihet [8]), Z-contractions (by Shukla ) and Tirado contraction ([16]), which are for only one self map. Using this, we establish a unique common fixed point theorem for two self maps satisfying condition (S), which was introduced by Shukla et al. in through weak compatibility. The article includes an example, which shows the validity of our results. 2010 Mathematics Subject Classification. 47H10.
Journal of Nonlinear Sciences and Applications, 2012
The object of this paper is to establish a generalized form of Banach contraction principle for a... more The object of this paper is to establish a generalized form of Banach contraction principle for a cone metric space which is not necessarily normal. This happens to be a generalization of all different forms of Banach contraction Principle, which have been arrived at in L.
The object of this paper is to establish a unique common fixed point theorem for a sequence of se... more The object of this paper is to establish a unique common fixed point theorem for a sequence of self mappings in a fuzzy metric space, which generalizes the result of Grabiec [3], Singh and Jain [5] and Vasuki [7]. All the results established in this paper are new.
In (1), A. Branciari defines a Generalised metric space of finite order �# and establishes Banach... more In (1), A. Branciari defines a Generalised metric space of finite order �# and establishes Banach contraction principle in it. The object of this paper is to extend this result to Quasi contraction and prove some fixed point results for two weakly compatible self maps satisfying a generalized contractive condition in this space without assuming it to be Hausdorff . Our result generalizes the said result of (1). All the results presented in this paper are new.
Abstract. This paper introduces the notion of semi-compatible self-maps in 2-metric spaces and es... more Abstract. This paper introduces the notion of semi-compatible self-maps in 2-metric spaces and establishes a fixed point theorem for four self-maps, satisfying an implicit relation through semi-compatibility of a pair of self-maps. This results in another fixed point ...
The aim of this paper is to introduce the notion of interpolative fuzzy Z-contractive condition f... more The aim of this paper is to introduce the notion of interpolative fuzzy Z-contractive condition for a pair of self maps in a fuzzy metric space, which enlarges, unifies and generalizes the existing fuzzy contractions (by Gregori and Sapena [6]), ψ contraction (by Mihet [11]), fuzzy Z-contractions (by Shukla et al. [21]) and Tirado contraction (by Tirado [22]), which are for only one self map. Using this, we establish a unique common fixed point theorem for two self maps satisfying condition (S), which was introduced by Shukla et al. in [21] through weak compatibility. As an applications, we discuss fixed point theorem for Fredholm non-linear integral equation. The article also includes an example, which shows the validity of our results.
Introduction/purpose: The aim of this paper is to introduce the notion of an interpolative genera... more Introduction/purpose: The aim of this paper is to introduce the notion of an interpolative generalised Meir-Keeler contractive condition for a pair of self maps in a fuzzy metric space, which enlarges, unifies and generalizes the Meir-Keeler contraction which is for only one self map. Using this, we establish a unique common fixed point theorem for two self maps through weak compatibility. The article includes an example, which shows the validity of our results. Methods: Functional analysis methods with a Meir-Keeler contraction. Results: A unique fixed point for self maps in a fuzzy metric space is obtained. Conclusions: A fixed point of the self maps is obtained.
International Journal of Engineering Sciences, 2021
Graphene-enabled nano antennas constitute a novel paradigm which is a current trend of research a... more Graphene-enabled nano antennas constitute a novel paradigm which is a current trend of research among designers. Graphene-based nano-antennas with nanometer in size have shown to radiate electromagnetic waves at the terahertz (THz) frequency band. Proposed research activity is an attempt of Terahertz Nano dipole antenna design through the Finite Difference Time Domain (FDTD) based numerical simulation software, i.e. CST. Graphene material as adipole antenna has been explored to get a radiation performance. Before hand absorption, reflection and transmission characteristics of the grapheme layer has been explored. Designed antenna is analyzed in terms of the reflection coefficient, and radiation pattern etc. An attempt has been done for resonance study of graphene based nano dipole antennas, in that patch antenna length parameteris changed and performance is observed. The impact of most crucial parameter, i.e., chemical potential on the grapheme radiation performance has been analyze...
The object of this paper is to introduce the concept of compatibility of pair of self maps in a c... more The object of this paper is to introduce the concept of compatibility of pair of self maps in a cone metric space without assuming its normality. Using this concept we establish a unique common fixed point theorem for four self maps satisfying a generalized contractive ...
The object of this paper is to introduce the notion of semi-compatible maps in fuzzy metric space... more The object of this paper is to introduce the notion of semi-compatible maps in fuzzy metric spaces, fuzzy 2-metric spaces and fuzzy 3-metric spaces and to establish three common fixed point theorems for these spaces for four self-maps. These results improve, extend and generalize the results of [16]. As an application , these results have been used to obtain translation and generalization of Grabeic's contraction principle in the new settings. All the result presented in this paper are new.
Journal of Nonlinear Sciences and Applications, 2010
The object of this paper is to establish unique common fixed point theorems for four self maps sa... more The object of this paper is to establish unique common fixed point theorems for four self maps satisfying a new contractive condition in a modified intuitionistic fuzzy metric space through compatibility of type (P). A generalization of a result of D Turkoglu et al [J. Apply. Math. Computing (2006)] in the setting of a modified intuitionistic fuzzy metric space follows from them. Modified intuitionistic fuzzy version of Grabiec contraction Principle has also been established. All the results presented in this paper are new. Examples have been constructed in support of the main results of this paper.
B. Singh and R. K. Sharma [Demonstratio Math. Vol. 36, No.l (2003), 215-220] have proved two comm... more B. Singh and R. K. Sharma [Demonstratio Math. Vol. 36, No.l (2003), 215-220] have proved two common fixed point theorems for two self-maps satisfying an expansive condition in Dmetric spaces. This note offers generalization for these theorems for three self-maps using weakcompatibility and reduces the domain of ζ to an orbit only. The last theorem proves that the continuity of none of two or three maps is required in the setting of Dmetric space.
This paper deals with a general contraction. Two fixed-point theorems for a limit weak-compatible... more This paper deals with a general contraction. Two fixed-point theorems for a limit weak-compatible pair of a multi-valued map and a self map on a D-metric space have been established. These results improve significantly, the main results of Dhage, Jennifer and Kang [5] by reducing its assumption and generalizing its contraction simultaneously. At the same time some results of Singh, Jain and Jain [12] are generalized from a self map to a pair of a set-valued and a self map. Theorems of Veerapandi and Rao [16] get generalized and improved by these results. All the results of this paper are new.
The aim of this paper is to introduce fuzzy generalised weak contractive condition for a pair of ... more The aim of this paper is to introduce fuzzy generalised weak contractive condition for a pair of self maps in a fuzzy metric space,which is in accordance with the theory of metric spaces given by Rhoades (Nonlinear Analysis 47:2683–2693, 2001). Our results generalize existing fuzzy contraction (by Gregori and Sapena (Fuzzy Sets System 125:245–252, 2002), which is for only one self map. Using this, we establish a unique common fixed point theorem for two self-maps through weak compatibility. The article includes an example, in support of our results. Also an application we established, for the existence and uniqueness of a solution of Fredholm non-linear integral equation in the setting of fuzzy metric space.
The object of this paper is to establish a unique common fixed point theorem for six self-mapping... more The object of this paper is to establish a unique common fixed point theorem for six self-mappings satisfying a generalized contractive condition through compatibility of type (β) and weak compatibility in a fuzzy metric space. It significantly generalizes the result of Singh and Jain [The Journal of Fuzzy Mathematics (2006)] and Sharma [Fuzzy Sets and Systems (2002)]. An example has been constructed in support of our main result. All the results presented in this paper are new.
The aim of this paper is to introduce Zs-contractive condition for a pair of self maps in a fuzzy... more The aim of this paper is to introduce Zs-contractive condition for a pair of self maps in a fuzzy metric space, which enlarges and unifies the existing fuzzy contractions (by Gregori and Sapena [4]), ψcontraction (by Mihet [8]), Z-contractions (by Shukla ) and Tirado contraction ([16]), which are for only one self map. Using this, we establish a unique common fixed point theorem for two self maps satisfying condition (S), which was introduced by Shukla et al. in through weak compatibility. The article includes an example, which shows the validity of our results. 2010 Mathematics Subject Classification. 47H10.
Journal of Nonlinear Sciences and Applications, 2012
The object of this paper is to establish a generalized form of Banach contraction principle for a... more The object of this paper is to establish a generalized form of Banach contraction principle for a cone metric space which is not necessarily normal. This happens to be a generalization of all different forms of Banach contraction Principle, which have been arrived at in L.
The object of this paper is to establish a unique common fixed point theorem for a sequence of se... more The object of this paper is to establish a unique common fixed point theorem for a sequence of self mappings in a fuzzy metric space, which generalizes the result of Grabiec [3], Singh and Jain [5] and Vasuki [7]. All the results established in this paper are new.
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