Development of Fixed Point Results for αΓ-F-Fuzzy Contraction Mappings with Applications

Sessa, Salvatore; Jahangeer, Fahad; Kattan, Doha A.; Ishtiaq, Umar

doi:10.3390/sym15071300

Cited by 3 publications

(1 citation statement)

References 14 publications

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“…Even in the present time, for the benefit of human beings, researchers of several fields including computers, physics, applied mathematics, and many others are benefiting from using the Banach contraction principle. Sessa et al [3] demonstrated some FP results and provided an application for nonlinear differential equation. In 1968, Kannan [4] gave some FP results and enhanced the era of fixed point theory.…”

Section: Introductionmentioning

confidence: 99%

Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications

Jahangeer,

Alshaikey,

Ishtiaq

et al. 2023

Fractal Fract

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In this manuscript, we present several types of interpolative proximal contraction mappings including Reich–Rus–Ciric-type interpolative-type contractions and Kannan-type interpolative-type contractions in the setting of bipolar metric spaces. Further, taking into account the aforementioned mappings, we prove best proximity point results. These results are an extension and generalization of existing ones in the literature. Furthermore, we provide several nontrivial examples, an application to find the solution of an integral equation, and a nonlinear fractional differential equation to show the validity of the main results.

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Section: Introductionmentioning

confidence: 99%

Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications

Jahangeer,

Alshaikey,

Ishtiaq

et al. 2023

Fractal Fract

Self Cite

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Fixed-Point Results for Mappings Satisfying Implicit Relation in Orthogonal Fuzzy Metric Spaces

Sonam,

Rathore,

Pal

et al. 2023

Advances in Fuzzy Systems

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This research paper introduces a comprehensive study on fixed points in orthogonal fuzzy metric spaces. The primary objective is to establish the existence and uniqueness of fixed points for self-mappings satisfying implicit relation criteria in complete orthogonal fuzzy metric spaces. By doing so, our proven results extend and generalise well-known findings in the field of fixed-point theory. To demonstrate the significance of the established results, several related examples are provided, serving to support and validate the theoretical findings in orthogonal fuzzy metric spaces. The implications of these results are discussed, shedding light on their potential applications in various practical scenarios. In addition to theoretical advancements, the paper also demonstrates a practical application of our established results in solving integral equations. This application exemplifies the effectiveness and versatility of the proposed approach in real-world problem-solving scenarios.

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New L-fuzzy fixed point techniques for studying integral inclusions

Shagari,

Alotaibi,

Aydi

et al. 2024

J Inequal Appl

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The survey of the available literature shows that a lot of important invariant point problems of Banach and Heilpern types have been examined in both metric and quasimetric spaces. However, a handful of the existing results employed the recent approaches of interpolative contractions. Therefore, based on the new idea of interpolation techniques in fixed point theory, this article studies new notions of L-fuzzy contractions and investigates conditions for the existence of L-fuzzy fixed points for such mappings. On the fact that fixed points of point-to-point mappings satisfying interpolative-type contraction are not always unique, whence making the concepts more fitted for invariant point results of crisp set-valued maps, new multi-valued analogues of the key findings put forward in this work are derived. Comparative illustrations, which indicate the preeminence of the results presented herein, are constructed. From application viewpoint, one of the theorems so obtained is employed to introduce new solvability conditions of Fredholm-type integral inclusions.

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Development of Fixed Point Results for αΓ-F-Fuzzy Contraction Mappings with Applications

Cited by 3 publications

References 14 publications

Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications

Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications

Fixed-Point Results for Mappings Satisfying Implicit Relation in Orthogonal Fuzzy Metric Spaces

New L-fuzzy fixed point techniques for studying integral inclusions

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