On Proximity and Fixed Point Theorem for Semi Contractions of E-Metric Space

Abstract

In this paper, we investigate some theorems on the existence and convergence of best proximity point for a semi-cyclic contraction pair (S,T) in the setting of non solid cone E-metric space with empty interior containing semi-interior points which poses larger class of metric spaces. further we apply our finding results in the E-cone metric space to prove the existence of the solution of certain integral equation.

Keywords: Positive non solid cone; semi-interior point; fixed point; best proximity point.

2010 Mathematics Subject Classification. 47H10; 46B40; 54H25