Coupled fixed points and coupled best proximity points for cyclic Ćirić type operators

Abstract

The purpose of this paper is to study the coupled fixed point problem and the coupled best proximity problem for single-valued and multi-valued contraction type operators defined on cyclic representations of the space. The approach is based on fixed point results for appropriate operators generated by the initial problems.

The Best Proximity Point Problem for New Types of Ciric a 􀀀b􀀀 Contraction with Application

“…Anuradha and Veeramani (6) proved the existence of a best proximity point for proximal pointwise contraction. Recently many authors have studied and generalize various concept related to the best proximity points (7)(8)(9)(10)(11)(12)(13)(14) .…”

“…) if {x n } be a sequence in A such that α(x n , x n+1 ) ≥ 1 and {x n(k) } of {x n } such that α(x n , x n+1 ) ≥ 1 for all k(A, d, R) is regular;(6) there exist α − β contractive;(7) φ is continuous, β > max {α 2 , α 3 }, then T has a best proximity point x…”