Some best proximity point results via a new family of F-contraction and an application to homotopy theory

Aslantaş, Mustafa

doi:10.1007/s11784-021-00895-9

Cited by 11 publications

(3 citation statements)

References 36 publications

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“…Anuradha and Veeramani (6) proved the existence of a best proximity point for proximal pointwise contraction. Recently many authors have studied and generalize various concept related to the best proximity points (7)(8)(9)(10)(11)(12)(13)(14) .…”

Section: Introductionmentioning

confidence: 99%

The Best Proximity Point Problem for New Types of Ciric a 􀀀b􀀀 Contraction with Application

Tiwari,

Dewangan

2023

IJST

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Objectives: To generate the best proximity point theorem for new types of Ciric α − β − contraction. Methods: By using generalized α − β − proximal quasi contraction and Ciric type G-contraction. Findings: We made new types of Ciric α − β − contraction. Novelty/Improvement: we give new types of Ciric α − β −contraction which is a generalization of generalized α − β − proximal quasi contraction and Ciric type G-contraction.

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Section: Introductionmentioning

confidence: 99%

The Best Proximity Point Problem for New Types of Ciric a 􀀀b􀀀 Contraction with Application

Tiwari,

Dewangan

2023

IJST

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“…Additionally, a best proximity point turns into a fixed point in the case of D = E = Λ. Therefore, many authors have studied on this topic [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

A New Best Proximity Point Result with an Application to Nonlinear Fredholm Integral Equations

Şahin

2022

Mathematics

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In the current paper, we first introduce a new class of contractions via a new notion called p-cyclic contraction mapping by combining the ideas of cyclic contraction mapping and p-contraction mapping. Then, we give a new definition of a cyclically 0-complete pair to weaken the completeness condition on the partial metric spaces. Following that, we prove some best proximity point results for p-cyclic contraction mappings on D∪E where D,E is a cyclically 0-complete pair in the setting of partial metric spaces. Hence, we generalize and unify famous and well-known results in the literature of metric fixed point theory. Additionally, we present some nontrivial examples to compare our results with earlier. Finally, we investigate the sufficient conditions for the existence of a solution to nonlinear Fredholm integral equations by the results in the paper.

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“…There exist too many studies on fixed-point theory in different spaces [1][2][3][4][5][6][7][8][9][10][11][12]. Also, there are many applications of the theory and mappings that meet certain conditions of contraction and have been a crucial area of different research works.…”

Section: Introductionmentioning

confidence: 99%

On Fixed Point Results for Generalized Contractions in Non-Newtonian Metric Spaces

Binbaşıoǧlu

2022

Cumhuriyet Science Journal

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TThe work of non-Newtonian calculus was begun in 1972. This calculus provides a different area to the classical one. Non-Newtonian metric concept was defined in 2002 by Basar and Cakmak. Then Binbaşıoğlu et al. had given the metric spaces of non-Newtonian in 2016. Also, they started to the fixed-point theory by defining some topological properties in non-Newtonian metric spaces. In this work, we give some fixed-point theorems and results for self-mappings satisfying certain conditions in the non-Newtonian metric spaces.

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Some best proximity point results via a new family of F-contraction and an application to homotopy theory

Cited by 11 publications

References 36 publications

The Best Proximity Point Problem for New Types of Ciric a 􀀀b􀀀 Contraction with Application

The Best Proximity Point Problem for New Types of Ciric a 􀀀b􀀀 Contraction with Application

A New Best Proximity Point Result with an Application to Nonlinear Fredholm Integral Equations

On Fixed Point Results for Generalized Contractions in Non-Newtonian Metric Spaces

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