Approximate Best Proximity Pairs in Metric Space

Abstract

Let A and B be nonempty subsets of a metric space X and also T :for some > 0. We call pair A, B an approximate best proximity pair. In this paper, definitions of approximate best proximity pair for a map and two maps, their diameters, T -minimizing a sequence are given in a metric space.

Approximate Best Proximity Pairs in Fuzzy Normed Spaces for Contraction Maps

“…In this paper starting from the article of Mohsenalhosseini and Mazaheri [12], we study some well known types of operators on fuzzy normed spaces, and we give some qualitative and quantitative results regarding approximate best proximity pairs of such operators.…”

Approximate fixed point theorems of cyclical contraction mapping

“…In 2011, Mohsenalhosseini et al [6], introduced the approximate best proximity pairs and proved the approximate best proximity pairs property for it. Also, In 2012 , Mohsenalhosseini et al [7], introduced the approximate fixed point for completely norm space and map T α and proved the approximate fixed point property for it.…”

“…Also, In 2012 , Mohsenalhosseini et al [7], introduced the approximate fixed point for completely norm space and map T α and proved the approximate fixed point property for it. In 2014 , Mohsenalhosseini [8] introduced the Approximate best proximity pairs on metric space for contraction maps. This paper, on the other hand aims at introducing the new classes of cyclical operators and contraction maps (not necessarily continuous) regarding approximate fixed point on metric spaces.…”

Some Results of Best Proximity Point in Regular Cone Metric Spaces

“…Best proximity point theory of cyclic contraction maps has been studied by many authors see [1,3,9] and references therein. In 2007, Huang and Zhang [6] introduced cone metric spaces as a generalization of metric spaces.…”