On Pata–Suzuki-Type Contractions

Alqahtani, Obaid; Himabindu, Venigalla Madhulatha; Karapınar, Erdal

doi:10.3390/math7080720

Cited by 10 publications

(7 citation statements)

References 16 publications

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“…In his already classical article [14], Suzuki presented an elegant generalization of Banach's contraction principle that he used to characterize complete metric spaces. Although Suzuki's theorem has been successfully generalized and extended in several directions and contexts (see, e.g., [15][16][17][18][19][20][21][22][23][24][25][26][27][28]) we here show by means of an easy example that its full extension to the framework of w-distances presents suggestive difficulties that we think deserve attention.…”

Section: Introductionmentioning

confidence: 88%

Presymmetric w-Distances on Metric Spaces

Romaguera,

Tirado

2023

Preprint

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In an outstanding article published in 2008, Suzuki obtained a nice generalization of the Banach contraction principle from which derived a characterization of metric completeness. Although Suzuki’s theorem has been successfully generalized and extended in several directions and contexts, we here show by means of a simple example that the problem of achieving, in an obvious way, its full extension to the framework of w-distances does not have an emphatic response. Motivated by this fact we introduce the concept of presymmetric w-distance on metric spaces, we give some properties and examples of this new structure and show that it provides a reasonable setting to obtain a real and hardly forced w-distance generalization of Suzuki’s theorem. This is realized in our main result, which is a fixed point theorem that involves presymmetric w-distances and certain contractions of Suzuki-type. We also discuss the relationship between our main result and the well-known w-distance full generalization of the Banach contraction principle, due to Suzuki and Takahashi. Connected to this approach we prove another fixed point result that compare with our main result through some examples. Finally, we state a characterization of metric completeness by using our fixed point results.

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Section: Introductionmentioning

confidence: 88%

Presymmetric w-Distances on Metric Spaces

Romaguera,

Tirado

2023

Preprint

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“…Among them are two contractive conditions presented by V. Pata [7] and T. Suzuki [8], which shall be discussed here. Recently, Karapınar et al in [9] modified these contractive conditions and proved some fixed-point results by introducing a new type of contraction called the α-Pata-Suzuki-type contraction. Geraghty [10] proposed another extension of the Banach contraction principle, known as the Geraghty contraction.…”

Section: Introductionmentioning

confidence: 99%

Geraghty–Pata–Suzuki-Type Proximal Contractions and Related Coincidence Best Proximity Point Results

Saleem,

Raazzia,

Hussain

et al. 2023

Symmetry

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The objective of this research paper is to establish the existence and uniqueness of the best proximity and coincidence with best proximity point results, specifically focusing on Geraghty–Pata–Suzuki-type proximal mappings. To achieve this, we introduce three types of mappings, all within the context of a complete metric space: an α−θ−Geraghty–Pata–Suzuki-type proximal contraction; an α−θ−generalized Geraghty–Pata–Suzuki-type proximal contraction; and an α−θ−modified Geraghty–Pata–Suzuki-type proximal contraction. These new results generalize, extend, and unify various results from the existing literature. Symmetry plays a crucial role in solving nonlinear problems in operator theory, and the variables involved in the metric space are symmetric. Several illustrative examples are provided to showcase the superiority of our results over existing approaches.

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“…Recently, Pata contraction has been studied by many authors. Some of the studies were for Pata contraction presented by [3][4][5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

“…Karapinar et al [11] introduced Pata-Ciric type contraction at a point. Alqahtani et al [5] gave the α-Pata-Suzuki contraction and fixed point results for such contractions. After that, Karapinar and Himabindu [11] proved some common fixed point results for Pata-Suzuki Z-contraction.…”

Section: Introductionmentioning

confidence: 99%

On Pata Convex-Type Contractive Mappings

Aktay

Özdemir

2022

Journal of Function Spaces

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In this work, we introduce weak Pata convex contractions and weak E -Pata convex contractions via simulation functions in metric spaces to prove some fixed point results for such mappings. Also, we consider an example related to weak Pata convex contractions. Consequently, our results generalize and unify some results in the literature.

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On Pata–Suzuki-Type Contractions

Cited by 10 publications

References 16 publications

Presymmetric w-Distances on Metric Spaces

Presymmetric w-Distances on Metric Spaces

Geraghty–Pata–Suzuki-Type Proximal Contractions and Related Coincidence Best Proximity Point Results

On Pata Convex-Type Contractive Mappings

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