Feng–Liu type approach to best proximity point results for multivalued mappings

Şahin, Hakan; Aslantaş, Mustafa; Altun, İshak

doi:10.1007/s11784-019-0740-9

Cited by 38 publications

(21 citation statements)

References 23 publications

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“…It is clear that inequality (7) reduces to inequality (3) when l � 0. Similarly, inequality (7) reduces to inequality (5) when p � 1 and l � r − 1.…”

Section: Definition 1 (General Higher-order Lipschitz Mappings) a Mapping Tmentioning

confidence: 99%

General Higher-Order Lipschitz Mappings

Gordon

2021

Journal of Mathematics

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“…It is clear that inequality (7) reduces to inequality (3) when l � 0. Similarly, inequality (7) reduces to inequality (5) when p � 1 and l � r − 1.…”

Section: Definition 1 (General Higher-order Lipschitz Mappings) a Mapping Tmentioning

confidence: 99%

General Higher-Order Lipschitz Mappings

Gordon

2021

Journal of Mathematics

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“…&, 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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Feng–Liu type approach to best proximity point results for multivalued mappings

Cited by 38 publications

References 23 publications

General Higher-Order Lipschitz Mappings

General Higher-Order Lipschitz Mappings

Best proximity point theory on vector metric spaces

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

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Feng–Liu type approach to best proximity point results for multivalued mappings

Cited by 38 publications

References 23 publications

General Higher-Order Lipschitz Mappings

General Higher-Order Lipschitz Mappings

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