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

Abstract

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.

Keywords

• Best proximity point
• Cyclic contraction
• Hardy–Rogers cyclic contraction
• p-proximal contraction
• Uniform spaces