Best proximity point results for Hardy–Rogers p-proximal cyclic contraction in uniform spaces

Abstract

The Hardy-Rogers p-proximal cyclic contraction, which includes the cyclic, Kannan, Chatterjea and Reich contractions as sub-classes, is developed in uniform spaces. The existence and uniqueness results of best proximity points for these contractions are proved. The results, which are for non-self maps, apart from the fact that they are new in literature, generalise several other similar results in literature. Examples are given to validate the results obtained. MSC: 47H10; 54H25

Geraghty Contractions in Ordered Uniform Spaces

“…Recently, Olisama et.al. proved best proximity results in uniform spaces [6,7]. (Also see [8,9,10,11]).…”

A fixed point theorem for Hardy-Rogers type on generalized fractional differential equations

“…A new direction to the literature of common xed point theorems related to T -Hardy-Rogers contraction mappings, Banach pair of mappings, and cone metric space due to Rhymend in [42]. A modied class of Hardy-Rogers p-proximate cyclic contraction in uniform spaces was introduced by Olisama in [36]. Abbas in [1] proved some xed point theorems for a T -Hardy-Rogers contraction in the setting of partially ordered partial metric spaces.…”