g-approximate best proximity pairs in metric space with a directed graph [PDF]
arXivLet(X,d) be a metric space that has a directed graph G such that the sets V(G) and E(G) are respectively vertices and edges corresponding to X. We obtain sufficient conditions for the existence of an G-approximate best proximity pair of the mapping T in the metric space X endowed with a graph G such that the set V(G) of vertices of G coincides with X.
Mohsenialhosseini, Saheli
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b-metric spaces and the related approximate best proximity pair results using contraction mappings
Advances in Fixed Point Theory: The aim of this paper is to prove some new approximate best proximity pair theorems on b -metric spaces using contraction mappings, including P -Bianchini contraction, P − B contraction, etc.
K. Saravanan, V. Piramanantham
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Common best proximity point theorems under proximal $F$-weak dominance in complete metric spaces [PDF]
arXiv, 2022 Suppose that $S_1$ and $S_2$ are nonempty subsets of a complete metric space $(\mathcal{M},d)$ and $\phi,\psi:S_1\to S_2$ are mappings. The aim of this work is to investigate some conditions on $\phi$ and $\psi$ such that the two functions, one that assigns to each $x\in S_1$ exactly $d(x,\phi x)$ and the other that assigns to each $x\in S_1$ exactly ...
A. Deep, R. Batra
arxiv +3 more sources
Generalized Cyclic p-Contractions and p-Contraction Pairs Some Properties of Asymptotic Regularity Best Proximity Points, Fixed Points [PDF]
Symmetry, 2022 This paper studies a general p-contractive condition of a self-mapping T on X, where (X,d) is either a metric space or a dislocated metric space, which combines the contribution to the upper-bound of d(Tx, Ty), where x and y are arbitrary elements in X ...
Manuel De la Sen, Asier Ibeas
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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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Generalized common best proximity point results in fuzzy multiplicative metric spaces
AIMS Mathematics, 2023 In this manuscript, we prove the existence and uniqueness of a common best proximity point for a pair of non-self mappings satisfying the iterative mappings in a complete fuzzy multiplicative metric space.
Umar Ishtiaq +3 more
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FilomatIn the setup of metric spaces, many recent studies established a significant variety of control type mappings and illustrated some fixed point results. To represent various contractivity conditions, Khojasteh et al.
P PaunovicMarija +2 more
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Best proximity pair results for relatively nonexpansive mappings in geodesic spaces [PDF]
arXiv, 2013 Given $A$ and $B$ two nonempty subsets in a metric space, a mapping $T : A \cup B \rightarrow A \cup B$ is relatively nonexpansive if $d(Tx,Ty) \leq d(x,y) \text{for every} x\in A, y\in B.$ A best proximity point for such a mapping is a point $x \in A \cup B$ such that $d(x,Tx)=\text{dist}(A,B)$.
Aurora Fernández León, Adriana Nicolae
arxiv +3 more sources
Best Proximity Pair Theorems for Multifunctions with Open Fibres
, 2000 Let A and B be non-empty subsets of a normed linear space, and f:A->B be a single valued function. A solution to the functional equation fx=x, (x@?A) will be an element x"o in A such that fx"o=x"o (i.e., such that d(fx, x)=0).
S. Sadiq Basha, P. Veeramani
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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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