Existence and convergence of best proximity points
By A. A. Eldred, P. Veeramani. 2006
671 citations recorded by the source corpus.
Abstract Consider a self map T defined on the union of two subsets A and B of a metric space and satisfying T ( A ) ⊆ B and T ( B ) ⊆ A . We give some contraction type existence results for a best proximity point, that is, a point x such that d ( x , T x ) = dist ( A , B ) . We also give an algorithm to find a best proximity point for the map T in the setting of a uniformly convex Banach space.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d06fd68a05ba8af57e945abb597c725e300802b4
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In Computational Theory and Mathematics
- Poom Kumam
- Wutiphol Sintunavarat
- Naseer Shahzad
- V. Sankar Raj
- S. Sadiq Basha
- Ancuţa Mihaela Petric
- Hakan Sahin
- Ishak Altun
In Geometry and Topology
- Poom Kumam
- Wutiphol Sintunavarat
- Ancuţa Mihaela Petric
- S. Sadiq Basha
- V. Sankar Raj
- Naseer Shahzad
- Ishak Altun
- Hakan Sahin
In Mathematical Physics
- S. Sadiq Basha
- Ancuţa Mihaela Petric
- V. Sankar Raj
- Naseer Shahzad
- Hakan Sahin
- Ishak Altun
- Mustafa Aslantas
- Poom Kumam
Citations in the corpus
- Best proximity pair theorems for relatively nonexpansive mappings (2009, methodology): “We make use of the main results proved in [3] to obtain best proximity pair theorems for relatively nonexpansive mappings.”
- Best proximity point theorems for cyclic p-contractions with some consequences and applications (2021, methodology): “Hence, by combining the ideas of both cyclic mapping and best proximity point Eldred and Veeremani [8] introduced the concept of cyclic contraction mapping and then obtained a result, which includes the situation A ∩B = ∅.”
- Best proximity point theorems for weak cyclic Kannan contractions (2011, methodology): “Inspired by the results in [2] and [3], we introduce the following class of cyclic contractive conditions which extends (3) for the case A ∩B = ∅.”
- Best proximity point theorems for generalized proximal contractions (2012, background): “Furthermore, many best proximity point theorems for several variants of contractions have been analyzed in [9-15].”
- Best Proximity Point Results for Modified --Proximal Rational Contractions (2013, neutral): “For more details on this approach, we refer the reader to [5, 7–32].”