Best proximity point results for p-proximal contractions

Altun, İshak; Aslantaş, Mustafa; Şahin, Hakan

doi:10.1007/s10474-020-01036-3

Cited by 49 publications

(40 citation statements)

References 16 publications

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“…Let (X; S) be an S-metric space, T : X ! X be an S-Pata type x 0 -mapping with x 0 2 X and be the real number de…ned in (1).…”

Section: Resultsmentioning

confidence: 99%

“…On the other hand, a related problem is the best proximity point problem since the best proximity point theorems investigate an optimal solution of the minimization problem fd (x; T x) : x 2 Ag for a mapping T : A ! B where A and B are two non-empty subsets of a metric space (see [1] and the references therein). In [6], the existence of best proximity point was investigated using the Pata type proximal mappings.…”

Section: Resultsmentioning

confidence: 99%

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On the geometry of fixed points of self-mappings on S-metric spaces

Özgür¹,

Taş²

2020

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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In this paper, we focus on some geometric properties related to the set F ix(T), the set of all …xed points of a mapping T : X ! X, on an S-metric space (X; S). For this purpose, we present the notions of an S-Pata type x 0mapping and an S-Pata Zam…rescu type x 0-mapping. Using these notions, we propose new solutions to the …xed circle (resp. …xed disc) problem. Also, we give some illustrative examples of our main results.

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“…Let (X; S) be an S-metric space, T : X ! X be an S-Pata type x 0 -mapping with x 0 2 X and be the real number de…ned in (1).…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

On the geometry of fixed points of self-mappings on S-metric spaces

Özgür¹,

Taş²

2020

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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show abstract

“…&, if there exists a sequence fa n g satisfying a n # 0 such that (& n ; &) a n for all n 2 N: (ii) The sequence f& n g is said to be E-Cauchy sequence if there exists a sequence fa n g satisfying a n # 0 such that (& n ; & n+p ) a n for all n; p 2 N: (iii) The vector metric space ( ; ; E) is said to be E-complete if every E-Cauchy sequence in E-converges to a point in . Because of these reasons, best proximity point theory is one of the area attracted the most attention lately [1,4,5,6,9,13,15,19,20].…”

Section: De…nition 2 ( [11]mentioning

confidence: 99%

Best proximity point theory on vector metric spaces

Şahin¹

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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In this paper, we …rst give a new de…nition of-Dedekind complete Riesz space (E;) in the frame of vector metric space (; ; E) and we investigate the relation between Dedekind complete Riesz space and our new concept. Moreover, we introduce a new contraction so called-vector proximal contraction mapping. Then, we prove certain best proximity point theorems for such mappings on vector metric spaces (; ; E) where (E;) is-Dedekind complete Riesz space. Thus, for the …rst time, we acquire best proximity point results on vector metric spaces. As a result, we generalize some …xed point results proved on both vector metric spaces and partially ordered vector metric spaces. Further, we provide nontrivial and comparative examples to show the e¤ectiveness of our main results.

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“…Hussain et al [12] established a generalized form of α− admissible mappings in order to prove coincidence points and common fixed points in the framework of G-metric spaces. Furthermore, several authors obtained different kinds of generalization of Banach contraction principle in different spaces (see for details [13][14][15][16][17][18][19][20]).…”

Section: (5)mentioning

confidence: 99%

On Generalized Rational $α -$ Geraghty Contraction Mappings in $G -$ Metric Spaces

Priyobarta

Khomdram

Rohen

et al. 2021

Journal of Mathematics

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In this paper, we discuss about various generalizations of α − admissible mappings. Furthermore, we extend the concept of α − admissible to generalize rational α − Geraghty contraction in G − metric space. With this new contraction mapping, we establish some fixed-point theorems in G − metric space. The obtained result is verified with an example.

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Best proximity point results for p-proximal contractions

Cited by 49 publications

References 16 publications

On the geometry of fixed points of self-mappings on S-metric spaces

On the geometry of fixed points of self-mappings on S-metric spaces

Best proximity point theory on vector metric spaces

On Generalized Rational $α -$ Geraghty Contraction Mappings in $G -$ Metric Spaces

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Best proximity point results for p-proximal contractions

Cited by 49 publications

References 16 publications

On the geometry of fixed points of self-mappings on S-metric spaces

On the geometry of fixed points of self-mappings on S-metric spaces

Best proximity point theory on vector metric spaces

On Generalized Rational α − Geraghty Contraction Mappings in G − Metric Spaces

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Product

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On Generalized Rational $α -$ Geraghty Contraction Mappings in $G -$ Metric Spaces