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Some results on best proximity pair theorems [PDF]
Applied General Topology, 2002 Best proximity pair theorems are considered to expound the sufficient conditions that ensure the existence of an element xo ϵ A, such that d(xo; T xo) = d(A;B) where T : A 2B is a multifunction defined on suitable subsets A and B of a normed linear ...
P.S. Srinivasan, P. Veeramani
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Strong and weak convergence of Ishikawa iterations for best proximity pairs [PDF]
Open Mathematics, 2020 Let A and B be nonempty subsets of a normed linear space X. A mapping T : A ∪ B → A ∪ B is said to be a noncyclic relatively nonexpansive mapping if T(A) ⊆ A, T(B) ⊆ B and ∥Tx − Ty∥ ≤ ∥x − y∥ for all (x, y) ∈ A × B.
Gabeleh Moosa +3 more
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Axioms, 2020 In this paper, we study a problem of global optimization using common best proximity point of a pair of multivalued mappings. First, we introduce a multivalued Banach-type contractive pair of mappings and establish criteria for the existence of their ...
Pradip Debnath, Hari Mohan Srivastava
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Cyclic pairs and common best proximity points in uniformly convex Banach spaces [PDF]
Open Mathematics, 2017 In this article, we survey the existence, uniqueness and convergence of a common best proximity point for a cyclic pair of mappings, which is equivalent to study of a solution for a nonlinear programming problem in the setting of uniformly convex Banach ...
Gabeleh Moosa +3 more
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On a generalization of a relatively nonexpansive mapping and best proximity pair
Fixed Point Theory and Algorithms for Sciences and Engineering, 2023 Let A and B be two nonempty subsets of a normed space X, and let T : A ∪ B → A ∪ B $T: A \cup B \to A \cup B$ be a cyclic (resp., noncyclic) mapping.
Karim Chaira, Belkassem Seddoug
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Convergence and Best Proximity Points for Generalized Contraction Pairs [PDF]
Mathematics, 2019 This paper is devoted to studying the existence of best proximity points and convergence for a class of generalized contraction pairs by using the concept of proximally-complete pairs and proximally-complete semi-sharp proximinal pairs.
Slah Sahmim +2 more
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Best proximity point (pair) results via MNC in Busemann convex metric spaces
Applied General Topology, 2022 In this paper, we present a new class of cyclic (noncyclic) α-ψ and β-ψ condensing operators and survey the existence of best proximity points (pairs) as well as coupled best proximity points (pairs) in the setting of reflexive Busemann convex spaces ...
Moosa Gabeleh, Pradip Ramesh Patle
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Diameter Approximate Best Proximity Pair in Fuzzy Normed Spaces [PDF]
Sahand Communications in Mathematical Analysis, 2019 The main purpose of this paper is to study the approximate best proximity pair of cyclic maps and their diameter in fuzzy normed spaces defined by Bag and Samanta.
Seyed Ali Mohammad Mohsenialhosseini +1 more
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Best proximity pair and fixed point results for noncyclic mappings in modular spaces
Arab Journal of Mathematical Sciences, 2018 In this paper, we formulate best proximity pair theorems for noncyclic relatively ρ-nonexpansive mappings in modular spaces in the setting of proximal ρ-admissible sets.
Karim Chaira, Samih Lazaiz
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Best proximity point results and application to a system of integro-differential equations
Advances in Difference Equations, 2021 In this work, we solve the system of integro-differential equations (in terms of Caputo–Fabrizio calculus) using the concepts of the best proximity pair (point) and measure of noncompactness.
Anupam Das +3 more
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