Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition

In this paper, we consider two families 1 and 2 of mappings defined on [0, +∞) satisfy some certain properties. Using the mentioned properties for 1 and 2 , we prove the analogous PPF dependent fixed point theorems for mappings as in Drici et al. (Nonlinear Anal. 67:641-647, 2007) in partially ordered Banach spaces where mappings satisfy the weaker contractive conditions without assuming the topological closedness with respect to the norm topology for the Razumikhin class R c . MSC: 54H25; 55M20

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“…All authors read and approved the final manuscript. 1 Department of Mathematics, Faculty of Science, Razi University, Kermanshah, 67149, Iran.…”

Section: Competing Interestsmentioning

confidence: 99%

On fixed point theorems for mappings with PPF dependence

Farajzadeh

Kaewcharoen

2014

J Inequal Appl

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“…The study of common fixed points of mappings satisfying certain contractive conditions can be employed to establish existence of solutions of certain operator equations such as differential and integral equations. Beg and Abbas [10] obtained common fixed points extending a weak contractive condition to two maps . In 2009, Dorić [17] proved common fixed point theorems for generalized ψ, φ -weakly contractive mappings.…”

Section: Introductionmentioning

confidence: 99%

Existence of common fixed point for b-metric rational type contraction

Abbas

Cheema

Razani

2016

Filomat

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Abstract.The necessary conditions for existence of a common fixed point of two mappings satisfying generalized b-order contractive condition in the setting of a partially ordered b-complete b-metric space are presented. Also, we study well-posedness of common fixed point problem for generalized b-order contractive mappings. We employ our result to establish an existence of a solution of an integral equation.

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“…There are examples that show that each of these generalizations of commutativity is a proper extension of the previous definition. On the other hand, Beg and Abbas [12] obtained a common fixed point theorem extending weak contractive condition for two maps. In this direction, Zhang and Song [51] introduced the concept of a generalized φ− weak contraction condition and obtained a common fixed point for two maps.…”

Section: Introductionmentioning

confidence: 99%

Common fixed point results of four mappings in ordered partial metric spaces

Nazır

Silvestrov

Abbas

2016

Waves, Wavelets and Fractals

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On partially ordered set equipped with a partial metric, we study the sufficient conditions for existence of common fixed points of various mappings satisfying generalized weak contractive conditions. These results unify several comparable results in the existing literature. We also study the existence of nonnegative solution of implicit nonlinear integral equation. Furthermore, we study the fractal of finite family of generalized contraction mappings defined on a partial metric space.

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Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition

Abstract: We prove the existence of coincidence point and common fixed point for mappings satisfying generalized weak contractive condition. As an application, related results on invariant approximation are derived. Our results generalize various known results in the literature.

Cited by 77 publications

References 15 publications

On fixed point theorems for mappings with PPF dependence

On fixed point theorems for mappings with PPF dependence

Existence of common fixed point for b-metric rational type contraction

Common fixed point results of four mappings in ordered partial metric spaces

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