A remark on the paper “A note on the paper Best proximity point results for p-proximal contractions”

A note on a paper "A regularization method for the proximal point algorithm"

In this note, a small gap is corrected in the proof of H.K. Xu [Theorem 3.3, A regularizationmethod for the proximal point algorithm, J. Glob. Optim. 36, 115–125 (2006)], and some strict restriction is removed also.

A note on the paper ‘Fixed point theorems for cyclic weak contractions in compact metric spaces’

Best Proximity Point Result for New Type of Contractions in Metric Spaces with a Graph

In this paper‎, ‎we introduce a new type of graph contraction using a special class of functions and give a best proximity point theorem for this contraction in complete metric spaces endowed with a graph under two different conditions‎. ‎We then support our main theorem by a non-trivial example and give some consequences of best proximity point of it for usual graphs.

Best Proximity Points for Weak Proximal Contractions

In this article, we introduce a new class of non-self mappings, called weak proximal contractions, which contains the proximal contractions as a subclass. Existence and uniqueness results of a best proximity point for weak proximal contractions are obtained. Also, we provide sufficient conditions for the existence of common best proximity points for two non-self mappings in metric spaces having...

Best Proximity Point Theorems for p-Cyclic Meir-Keeler Contractions

Meir and Keeler in 1 considered an extension of the classical Banach contraction theorem on a complete metric space. Kirk et al. in 2 extended the Banach contraction theorem for a class of mappings satisfying cyclical contractive conditions. Eldred and Veeramani in 3 introduced the following definition. Let A and B be nonempty subsets of a metric space X. A map T : A ∪ B → A ∪ B, is a cyclic co...