On common best proximity points for generalized α−ψ -proximal contractions

Abstract

We establish some common best proximity point results for generalized α − ψ-proximal contractive non-self mappings. We provide some concrete examples. We also derive some consequences on some best proximity results on a metric space endowed with a graph.

Best Proximity Point Theorems on Rectangular Metric Spaces Endowed with a Graph

“…From (17), d(x N+1 , x N ) = dist(A, B), we conclude that {d(x N+1 , x N )} N is a constant sequence equal to dist(A, B). Therefore, from (31), d(x * , f x * ) = dist(A, B).…”

“…There are many variants and extensions of results for the existence of a best proximity point. For more details, we refer to References [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Best proximity points for p-cyclic summing iterated contractions

“…We would like to finish with an open question. Is it possible to generalize the results about best proximity points in reflexive Banach spaces for other type of maps such as the investigated in [2][3][4][5]18]?…”

Common fixed point theorems for non-self mappings of nonlinear contractive maps in convex metric spaces

“…Many authors have proved the existence and uniqueness of common fixed points of contraction self mappings in metric spaces and its generalizations (see Karapinar [12], Abdeljawad et al [2], Aydi et al [6], Aydi et al [7]). Much work have been done on the approximation of fixed points of contraction mappings (see [3,14,15]).…”