Best proximity points for cyclic Meir–Keeler contractions

Bari, Cristina Di; Suzuki, Tomonari; Vetro, Calogero

doi:10.1016/j.na.2007.10.014

Cited by 198 publications

(74 citation statements)

References 8 publications

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“…Further, it is interesting to observe that best proximity theorems also emerge as a natural generalization of fixed point theorems, for a best proximity point reduces to a fixed point if the mapping under consideration is a self mapping. Investigation of several variants of contractions for the existence of a best proximity point can be found in [1,2,3,4,8,10,17,21,22]. Eldred et al [9] have established a best proximity point theorem for relatively non-expansive mappings.…”

Section: Theorem 112 ([6]mentioning

confidence: 99%

Some Results on Common Best Proximity Point and Common Fixed Point Theorem in Probabilistic Menger Space

Shayanpour¹

2016

Journal of the Korean Mathematical Society

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Abstract. In this paper, we define the concepts of commute proximally, dominate proximally, weakly dominate proximally, proximal generalized ϕ-contraction and common best proximity point in probabilistic Menger space. We prove some common best proximity point and common fixed point theorems for dominate proximally and weakly dominate proximally mappings in probabilistic Menger space under certain conditions. Finally we show that proximal generalized ϕ-contractions have best proximity point in probabilistic Menger space. Our results generalize many known results in metric space.

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Section: Theorem 112 ([6]mentioning

confidence: 99%

Some Results on Common Best Proximity Point and Common Fixed Point Theorem in Probabilistic Menger Space

Shayanpour¹

2016

Journal of the Korean Mathematical Society

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“…Cabellero et al [8] discussed the existence of a best proximity point of Geraghty contraction. The references [5,10,11,25,[27][28][29][30] furnish some appealing best proximity point theorems for various contractions while Basha [23] and Shahzad [26] explore some common best proximity point theorems for certain contractions.…”

Section: Introductionmentioning

confidence: 99%

Coincidence best proximity points for geraghty type proximal cyclic contractions

Komal¹,

Hussain²,

Sultana³

2018

J. Math. Computer Sci.

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In this paper, we study the notions of generalized Geraghty proximal cyclic contractions for non-self mapping and obtain coincidence best proximity point theorems in the framework of complete metric spaces. Some examples are given to show the validity of our results. Our results extended and unify many existing results in the literature.Keywords: α-Geraghty proximal contraction of first and second kind, α-proximal cyclic contraction, α-proximal admissible maps.

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“…It has also to be pointed out that the parallel background literature related to results on best proximity points and fixed points in cyclic mappings in metric and Banach spaces as well as topics related to common fixed points is exhaustive including studies of fixed point theory and applications in the fuzzy framework. See, for instance, [5,6,13,[17][18][19][20][21][22][23][24][25][26][27][31][32][33][34][35][36][37] as well as references therein.…”

Section: Introductionmentioning

confidence: 99%

Some results on best proximity points of cyclic alpha-psi contractions in Menger probabilistic metric spaces

Sen

Roldán

2017

Math Sci

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This paper investigates properties of convergence of distances of p-cyclic a-w-type contractions on the union of the p subsets of a space X defining probabilistic metric spaces and Menger spaces. The paper also investigates the characterization of both Cauchy and G-Cauchy sequences which are convergent, in particular, to best proximity points. On the other hand, the existence and uniqueness of fixed points and best proximity points of pcyclic a-w-type contractions are also investigated. The fixed points of the p-composite self-mappings, which are obtained from the p-cyclic self-mapping restricted to each of the p subsets in the cyclic disposal, are also investigated while a generalization and some illustrative examples are also given.

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Best proximity points for cyclic Meir–Keeler contractions

Cited by 198 publications

References 8 publications

Some Results on Common Best Proximity Point and Common Fixed Point Theorem in Probabilistic Menger Space

Some Results on Common Best Proximity Point and Common Fixed Point Theorem in Probabilistic Menger Space

Coincidence best proximity points for geraghty type proximal cyclic contractions

Some results on best proximity points of cyclic alpha-psi contractions in Menger probabilistic metric spaces

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