Best Proximity Point Iteration for Various types of Non Self Mappings

Abstract

This thesis explains the convergence results of Mann, Ishikawa and Thakur iterative newlineprocesses for best proximity points and common best proximity points of various newlinekinds of non-self mappings in the setting of Banach spaces. In detail, we approximate newlinea common fixed point for the class of relatively nonexpansive mappings by using newlineIshikawa iterative scheme. Through this result, we approximate common best newlineproximity points with the help of projective operators. And, we prove the newlineconvergence results of Mann and Ishikawa iterative processes on common best newlineproximity point for proximally mean nonexpansive mappings. Also, we construct newlineMann and Ishikawa iterative processes associated with multivalued mappings and newlinewe approach the best proximity point for nonexpansive, generalized nonexpansive newlineand proximally quasi-contractive multivalued mappings in uniformly convex Banach newlinespace. Finally, we use three-step iterative process, called Thakur iteration, to find a newlinecommon fixed point for the class of noncyclic relatively nonexpansive mappings and newlinethe consequence of our results, we approximate the common best proximity point newlinefor class of cyclic relatively nonexpansive mappings through our proposed Thakur newlineiterative process associated with projective operators. newline newline