Relation-theoretic contraction principle

Alam, Aftab; Imdad, Mohammad

doi:10.1007/s11784-015-0247-y

Cited by 154 publications

(213 citation statements)

References 11 publications

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“…Let X be a nonempty set and T be a self-mapping on X . A binary relation < defined on X is called T -closed if for any x; y 2 X , .x; y/ 2 < H) .T x; T y/ 2 <: Definition 2.6 ( [25]). Let X be a nonempty set and < be a binary relation on X .…”

Section: Definition 25 ([25]mentioning

confidence: 99%

Fixed point and multidimensional fixed point theorems with applications to nonlinear matrix equations in terms of weak altering distance functions

Sawangsup

Sintunavarat

2017

Open Mathematics

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Abstract:The aim of this work is to introduce the notion of weak altering distance functions and prove new fixed point theorems in metric spaces endowed with a transitive binary relation by using weak altering distance functions. We give some examples which support our main results where previous results in literature are not applicable. Then the main results of the paper are applied to the multidimensional fixed point results. As an application, we apply our main results to study a nonlinear matrix equation. Finally, as numerical experiments, we approximate the definite solution of a nonlinear matrix equation using MATLAB.

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Section: Definition 25 ([25]mentioning

confidence: 99%

Fixed point and multidimensional fixed point theorems with applications to nonlinear matrix equations in terms of weak altering distance functions

Sawangsup

Sintunavarat

2017

Open Mathematics

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“…(dq 1 Czerwik [10] proved Banach contraction theorem for single and multivalued mappings in b-metric spaces. Since then several fixed point results for various classes of single-valued and multivalued operators have been proved in the framework of b-metric spaces [10,11,29].…”

Section: Definition 12mentioning

confidence: 99%

Common fixed points of α-dominated multivalued mappings on closed balls in a dislocated quasi b-metric space

Alofi¹,

Al-Mazrooei²,

Leyew³

et al. 2017

J. Nonlinear Sci. Appl.

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In this paper, we introduce the concept of α-dominated multivalued mappings and establish the existence of common fixed points of such mappings on a closed ball contained in left/right K-sequentially complete dislocated quasi b-metric spaces. These results improve, generalize, extend, unify, and complement various comparable results in the existing literature. Our results not only extend some primary results to left/right K-sequentially dislocated quasi b-metric spaces but also restrict the contractive conditions on a closed ball only. Some examples are presented to support the results proved herein. Finally as an application, we obtain some common fixed point results for single-valued mappings by an application of the corresponding results for multivalued mappings satisfying the contractive conditions more general than Banach type and Kannan type contractive conditions on closed balls in a left K-sequentially complete dislocated quasi b-metric space endowed with an arbitrary binary relation.

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“…on metric space, many mathematician are doing their research during several years, see for example [4,5,9,[12][13][14]. Very recently, Alam and Imdad [2] presented relation-theoretic metrical fixed point results due to famous Banach contraction principle using an amorphous relation. No doubt their results extended and improved several comparable results in existing literature but still there are some cases where we can't explain the existence of fixed point employing their results.…”

Section: Introductionmentioning

confidence: 99%

“…Theorem 1.9. (Theorem 3.1, Alam and Imdad [2]) Let (X, d) be a complete metric space equipped with a binary relation R. Suppose T is a self-mapping on X such that…”

Section: Introductionmentioning

confidence: 99%

“…Before defining R-lower-semi-continuity, we look back on R-continuity of a function defined on a metric space equipped with an arbitrary binary relation R. Definition 1.13. [2] Let (X, d) be a metric space and R be a binary relation defined on X. A function f : X → X is said to be R-continuous at x if for every R-preserving sequence (x n ) converging to x, we have,…”

Section: Introductionmentioning

confidence: 99%

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Correction to: Relation-theoretic metrical fixed-point results via w-distance with applications

Senapati

Dey

2018

J. Fixed Point Theory Appl.

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In this article, utilizing the concept of w-distance, we prove the celebrated Banach's fixed point theorem in metric spaces equipped with an arbitrary binary relation. Necessarily our findings unveil another direction of relation-theoretic metrical fixed point theory. Also, our paper consists of several non-trivial examples which signify the motivation for such investigations. Finally, our obtained results enable us to explore the existence and uniqueness of solutions of nonlinear fractional differential equations involving the Caputo fractional derivative.2010 Mathematics Subject Classification. 47H10, 54H25.

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Relation-theoretic contraction principle

Cited by 154 publications

References 11 publications

Fixed point and multidimensional fixed point theorems with applications to nonlinear matrix equations in terms of weak altering distance functions

Fixed point and multidimensional fixed point theorems with applications to nonlinear matrix equations in terms of weak altering distance functions

Common fixed points of α-dominated multivalued mappings on closed balls in a dislocated quasi b-metric space

Correction to: Relation-theoretic metrical fixed-point results via w-distance with applications

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