Results 1 to 10 of about 130,379 (152)

Existence and Convergence Theorems of Best Proximity Points [PDF]

Journal of Applied Mathematics, 2013
The aim of this paper is to prove some best proximity point theorems for new classes of cyclic mappings, called pointwise cyclic orbital contractions and asymptotic pointwise cyclic orbital contractions.
Moosa Gabeleh, Naseer Shahzad
doaj   +3 more sources

Best Proximity Points for Some Classes of Proximal Contractions [PDF]

Abstract and Applied Analysis, 2013
Given a self-mapping and a non-self-mapping , the aim of this work is to provide sufficient conditions for the existence of a unique point , called g-best proximity point, which satisfies .
Maryam A. Alghamdi, Naseer Shahzad, Francesca Vetro   +2 more
doaj   +4 more sources

Generalized Proximal ψ-Contraction Mappings and Best Proximity Points [PDF]

Abstract and Applied Analysis, 2012
We generalized the notion of proximal contractions of the first and the second kinds and established the best proximity point theorems for these classes. Our results improve and extend recent result of Sadiq Basha (2011) and some authors.
Winate Sanhan, Chirasak Mongkolkeha, Poom Kumam   +2 more
doaj   +3 more sources

Best proximity points in ℱ-metric spaces with applications

Demonstratio Mathematica, 2023
The aim of this article is to introduce α\alpha -ψ\psi -proximal contraction in the setting of ℱ-metric space and prove the existence of best proximity points for these contractions.
Lateef Durdana
doaj   +2 more sources

Best proximity points of cyclic mappings

Applied Mathematics Letters, 2012
Let \(A\) and \(B\) be nonempty closed subsets of a complete metric space \((X,d)\). A map \(T: A \cup B \rightarrow A \cup B\) is called cyclic if \(T(A) \subset B\) and \(T(B) \subset A\). A point \(x \in A \cup B\) is called a best proximity point for \(T\) if \(d(x,T(x))\) coincides with the infimum of the set \(\{ d(a,b) : a \in A,\, b \in B \}\).
Erdal Karapinar
exaly   +3 more sources

Best Proximity Points for Alternative Maps [PDF]

Symmetry, 2019
Let ( X , d ) be a metric space and Ω i , i = 1 , 2 , … , m , be a nonempty subset of ( X , d ) . An operator T : ∪ 1 ≤ i ≤ m Ω i → ∪ 1 ≤ i ≤ m Ω i is called an alternative map if T ( Ω j ) ⊆ ∪ i ≠ j Ω i , j = 1 , 2 , … , m . In addition, if for any x, y ∈ ∪ 1 ≤ i ≤ m Ω i , there exists a constant α ∈ [ 0 , 1 ) such that d ( T x , T y ) ≤ α d ( x , y )
Yi Chou
exaly   +2 more sources

Results on the Existence and Convergence of Best Proximity Points [PDF]

Fixed Point Theory and Applications, 2010
We first consider a cyclic φ-contraction map on a reflexive Banach space X and provide a positive answer to a question raised by Al-Thagafi and Shahzad on the existence of best proximity points for cyclic φ-contraction maps in reflexive ...
Ali Abkar, Moosa Gabeleh
doaj   +4 more sources

Best Proximity Points for Cyclical Contractive Mappings

Applied General Topology, 2015
We consider p-cyclic mappings and prove an analogous result to Edelstien contractive theorem for best proximity points. Also we give similar results satisfying Boyd-Wong and Geraghty contractive conditions.
J. Maria Felicit, A. Anthony Eldred
doaj   +5 more sources

Best Proximity Points for K- Proximal Contraction

International Journal of Analysis and Applications, 2014
In this paper, we define K− proximal contraction and prove best proximity point theorem for this contraction. We also provide an illustrative example.
Ajay Sharma, Balwant Singh Thakur
doaj   +3 more sources

Best proximity points for alternative p-contractions

Journal of Inequalities and Applications
Cyclic mappings describe fixed paths for which each point is sequentially transmitted from one set to another. Cyclic mappings satisfying certain cyclic contraction conditions have been used to obtain the best proximity points, which constitute a ...
Mi Zhou, Nicolae Adrian Secelean, Naeem Saleem, Mujahid Abbas   +3 more
doaj   +3 more sources