Pant [Filomat 28 (2014), no. 2, 313-317] obtained some fixed point results in ultrametric spaces.... more Pant [Filomat 28 (2014), no. 2, 313-317] obtained some fixed point results in ultrametric spaces. Unfortunately, the proofs of main results had flaws. We present corrected proofs of his theorems for single valued mappings and correct formulations and proofs in the multivalued case.
In this paper, we explore (ϕ, L)-weak contractions of Berinde by obtaining Suzuki-type fixed poin... more In this paper, we explore (ϕ, L)-weak contractions of Berinde by obtaining Suzuki-type fixed point results. Thus, we obtain generalized fixed point results for Kannan's, Chatterjea's and Zamfirescu's mappings on a 0-complete partial metric space. In this way we obtain very general fixed point theorems that extend and generalize several related results from the literature.
We introduce a new variant of cyclic contractive mapping in a metric space and originate existenc... more We introduce a new variant of cyclic contractive mapping in a metric space and originate existence and uniqueness results of fixed points for such mappings. Examples are given to support the usability of our results. After these results, an application to integro-differential equations is given.
This paper extends and generalizes results of Mukheimer [(?,?,?)-contractive mappings in ordered ... more This paper extends and generalizes results of Mukheimer [(?,?,?)-contractive mappings in ordered partial b-metric spaces, J. Nonlinear Sci. Appl. 7(2014), 168-179]. A new concept of (?-?1-?2)-contractive mapping using two altering distance functions in ordered b-metric-like space is introduced and basic fixed point results have been studied. Useful examples are illustrated to justify the applicability and effectiveness of the results presented herein. As an application, the existence of solution of fourth-order two-point boundary value problems is discussed and rationalized by a numerical example.
We prove some coupled fixed point theorems for maps satisfying contractive conditions involving a... more We prove some coupled fixed point theorems for maps satisfying contractive conditions involving a rational expression in the setting of partially ordered metric spaces. We also present a result on the existence and uniqueness of coupled fixed points. An example is given to support the usability of our results, and to distinguish them from the known ones.
Existence of common fixed points for generalized S-nonexpansive subcompatible mappings in convex ... more Existence of common fixed points for generalized S-nonexpansive subcompatible mappings in convex metric spaces have been obtained. Invariant approximation results have also been derived by its application. These results extend and generalize various known results in the literature with the aid of more general class of noncommuting mappings.
We introduce the notion of cyclic generalized ϕ-contractive mappings in b-metric spaces and discu... more We introduce the notion of cyclic generalized ϕ-contractive mappings in b-metric spaces and discuss the existence and uniqueness of fixed points for such mappings. Our results generalize many existing fixed point theorems in the literature. Examples are given to support the usability of our results. Finally, an application to existence problem for an integral equation is presented. Definition 1.1. (Czerwik [8, 9]) Let X be a non-empty set and s ≥ 1 a real number. A function d : X × X → R + (nonnegative real numbers) is said to be a b-metric if, for all x, y, z ∈ X, (M1) d(x, y) = 0 if and only if x = y; (M2) d(x, y) = d(y, x); (M3) d(x, z) ≤ s[d(x, y) + d(y, z)]. The pair (X, d) is called a b-metric space with parameter s. Obviously, each metric space is a b-metric space (for s = 1). However, Czerwik [8, 9] has shown that a b-metric on X need not be a metric on X. The following simple examples can be used to show this.
We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obta... more We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obtain Kikkawa-Suzuki type fixed point theorems for a new type of generalized contractive conditions. Then, we prove data dependence of a fixed points set theorem. Finally, we present sufficient conditions for well-posedness of a fixed point problem. Our results generalize, complement and extend classical theorems in metric and partial metric spaces.
The purpose of this paper is to study modified S-iteration process and investigate the existence ... more The purpose of this paper is to study modified S-iteration process and investigate the existence and convergence theorems in the setting of CAT(0) spaces for a class of mappings which is wider than that of asymptotically nonexpansive mappings. Our results generalize, unify and extend several comparable results in the existing literature. MSC: 54H25; 54E40
Journal of Nonlinear Analysis and Application, 2013
The purpose of this paper is to prove some unified general common fixed point theorems employing ... more The purpose of this paper is to prove some unified general common fixed point theorems employing absorbing property for expansive mappings governed by a relatively improved implicit function in symmetric spaces which generalizes several previously known results due to Ali and Imdad [2], Djoudi [6], Imdad and Khan [15], Pathak and Tiwari [28], Popa [30] and some others. Some related results are also derived besides furnishing illustrative example.
Using the setting of TVS-valued ordered cone metric spaces (order is induced by a non normal cone... more Using the setting of TVS-valued ordered cone metric spaces (order is induced by a non normal cone), common fixed point results for four mappings satisfying implicit contractive conditions are obtained. These results extend, unify and generalize several well known comparable results in the literature.
Your article is protected by copyright and all rights are held exclusively by African Mathematica... more Your article is protected by copyright and all rights are held exclusively by African Mathematical Union and Springer-Verlag Berlin Heidelberg. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".
We introduce the notion of cyclic weakly Chatterjea type contraction and generalized cyclic weakl... more We introduce the notion of cyclic weakly Chatterjea type contraction and generalized cyclic weakly Chatterjea type contraction in metric spaces. We discussed the existence of fixed point theorems of (generalized) cyclic weakly Chatterjea type contraction mappings in the context of complete metric spaces. Our main theorems extend and improve some fixed point theorems in the literature.
Pant [Filomat 28 (2014), no. 2, 313-317] obtained some fixed point results in ultrametric spaces.... more Pant [Filomat 28 (2014), no. 2, 313-317] obtained some fixed point results in ultrametric spaces. Unfortunately, the proofs of main results had flaws. We present corrected proofs of his theorems for single valued mappings and correct formulations and proofs in the multivalued case.
In this paper, we explore (ϕ, L)-weak contractions of Berinde by obtaining Suzuki-type fixed poin... more In this paper, we explore (ϕ, L)-weak contractions of Berinde by obtaining Suzuki-type fixed point results. Thus, we obtain generalized fixed point results for Kannan's, Chatterjea's and Zamfirescu's mappings on a 0-complete partial metric space. In this way we obtain very general fixed point theorems that extend and generalize several related results from the literature.
We introduce a new variant of cyclic contractive mapping in a metric space and originate existenc... more We introduce a new variant of cyclic contractive mapping in a metric space and originate existence and uniqueness results of fixed points for such mappings. Examples are given to support the usability of our results. After these results, an application to integro-differential equations is given.
This paper extends and generalizes results of Mukheimer [(?,?,?)-contractive mappings in ordered ... more This paper extends and generalizes results of Mukheimer [(?,?,?)-contractive mappings in ordered partial b-metric spaces, J. Nonlinear Sci. Appl. 7(2014), 168-179]. A new concept of (?-?1-?2)-contractive mapping using two altering distance functions in ordered b-metric-like space is introduced and basic fixed point results have been studied. Useful examples are illustrated to justify the applicability and effectiveness of the results presented herein. As an application, the existence of solution of fourth-order two-point boundary value problems is discussed and rationalized by a numerical example.
We prove some coupled fixed point theorems for maps satisfying contractive conditions involving a... more We prove some coupled fixed point theorems for maps satisfying contractive conditions involving a rational expression in the setting of partially ordered metric spaces. We also present a result on the existence and uniqueness of coupled fixed points. An example is given to support the usability of our results, and to distinguish them from the known ones.
Existence of common fixed points for generalized S-nonexpansive subcompatible mappings in convex ... more Existence of common fixed points for generalized S-nonexpansive subcompatible mappings in convex metric spaces have been obtained. Invariant approximation results have also been derived by its application. These results extend and generalize various known results in the literature with the aid of more general class of noncommuting mappings.
We introduce the notion of cyclic generalized ϕ-contractive mappings in b-metric spaces and discu... more We introduce the notion of cyclic generalized ϕ-contractive mappings in b-metric spaces and discuss the existence and uniqueness of fixed points for such mappings. Our results generalize many existing fixed point theorems in the literature. Examples are given to support the usability of our results. Finally, an application to existence problem for an integral equation is presented. Definition 1.1. (Czerwik [8, 9]) Let X be a non-empty set and s ≥ 1 a real number. A function d : X × X → R + (nonnegative real numbers) is said to be a b-metric if, for all x, y, z ∈ X, (M1) d(x, y) = 0 if and only if x = y; (M2) d(x, y) = d(y, x); (M3) d(x, z) ≤ s[d(x, y) + d(y, z)]. The pair (X, d) is called a b-metric space with parameter s. Obviously, each metric space is a b-metric space (for s = 1). However, Czerwik [8, 9] has shown that a b-metric on X need not be a metric on X. The following simple examples can be used to show this.
We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obta... more We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obtain Kikkawa-Suzuki type fixed point theorems for a new type of generalized contractive conditions. Then, we prove data dependence of a fixed points set theorem. Finally, we present sufficient conditions for well-posedness of a fixed point problem. Our results generalize, complement and extend classical theorems in metric and partial metric spaces.
The purpose of this paper is to study modified S-iteration process and investigate the existence ... more The purpose of this paper is to study modified S-iteration process and investigate the existence and convergence theorems in the setting of CAT(0) spaces for a class of mappings which is wider than that of asymptotically nonexpansive mappings. Our results generalize, unify and extend several comparable results in the existing literature. MSC: 54H25; 54E40
Journal of Nonlinear Analysis and Application, 2013
The purpose of this paper is to prove some unified general common fixed point theorems employing ... more The purpose of this paper is to prove some unified general common fixed point theorems employing absorbing property for expansive mappings governed by a relatively improved implicit function in symmetric spaces which generalizes several previously known results due to Ali and Imdad [2], Djoudi [6], Imdad and Khan [15], Pathak and Tiwari [28], Popa [30] and some others. Some related results are also derived besides furnishing illustrative example.
Using the setting of TVS-valued ordered cone metric spaces (order is induced by a non normal cone... more Using the setting of TVS-valued ordered cone metric spaces (order is induced by a non normal cone), common fixed point results for four mappings satisfying implicit contractive conditions are obtained. These results extend, unify and generalize several well known comparable results in the literature.
Your article is protected by copyright and all rights are held exclusively by African Mathematica... more Your article is protected by copyright and all rights are held exclusively by African Mathematical Union and Springer-Verlag Berlin Heidelberg. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".
We introduce the notion of cyclic weakly Chatterjea type contraction and generalized cyclic weakl... more We introduce the notion of cyclic weakly Chatterjea type contraction and generalized cyclic weakly Chatterjea type contraction in metric spaces. We discussed the existence of fixed point theorems of (generalized) cyclic weakly Chatterjea type contraction mappings in the context of complete metric spaces. Our main theorems extend and improve some fixed point theorems in the literature.
Uploads
Papers by Hemant Nashine