On $\varphi$-Best Proximity Points and Proximal-type Algorithms in Banach Spaces

Abstract

The purpose of this paper is to study the existence and convergence of $\varphi$-best proximity points in Banach spaces. A strong convergence theorem is established by employing a shrinking projection algorithm designed to compute common $\varphi$-best proximity points of a proximally weakly suppressive mapping. Finally, we address a projection scheme to solve split $\varphi$-best proximity point and variational problem in a Banach space. These contributions provide new tools for solving nonlinear problems involving non-self mappings.