Some results on best proximity pair theorems

Abstract

Abstract. Best proximity pair theorems are considered to expound the sufficient conditions that ensure the existence of an elementB is a multifunction defined on suitable subsets A and B of a normed linear space E. The purpose of this paper is to obtain best proximity pair theorems directly without using any multivalued fixed point theorem. In fact, the well known Kakutani's fixed point theorem is obtained as a corollary to the main result of this paper. 2000

A Best Proximity Point Theorem for Generalized Non-Self-Kannan-Type and Chatterjea-Type Mappings and Lipschitzian Mappings in Complete Metric Spaces

“…For the previous research involving best proximity point theorems for several types of some mappings and contractions, one can refer to [7][8][9][10][11][12][13][14][15][16][17]. Best proximity point theorems for set valued mappings have been found in [18][19][20][21][22][23][24][25][26][27][28]. Moreover, in case of common best proximity point theorems, there are some interesting results in [29][30][31][32].…”