Best proximity points for generalized proximal C-contraction mappings in metric spaces with partial orders

Abstract

In this paper we extend the notion of weakly C-contraction mappings to the case of non-self mappings and establish the best proximity point theorems for this class. Our results generalize the result due to Harjani et al. (Comput. Math. Appl. 61:790-796, 2011) and some other authors.

Some Random Coupled Best Proximity Points for a Generalized ω-Cyclic Contraction in Polish Spaces

“…Subsequently, many researchers have studied the existence and convergence of best proximity point results in many ways [9,26,24,25,27,29,32,31].…”

A Coincidence Best Proximity Point Problem inG-Metric Spaces

“…This is an extension of the best proximity point problem. There are several results dealing with proximity point problem in the setup of metric spaces (see, e.g., [1][2][3][4][5][6][7][8][9][10][11] and references mentioned therein).…”

On Optimal Fuzzy Best Proximity Coincidence Points of Proximal Contractions Involving Cyclic Mappings in Non-Archimedean Fuzzy Metric Spaces

“…From a mathematical context, studies are available, for instance, in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and the references therein, following its introduction and characterization by Zadeh [4]. Among the research performed on the subject, effort has been devoted to the investigation of the existence and uniqueness of fixed points, best proximity points, fuzzy fixed points, fuzzy best proximity points, common fuzzy fixed points and optimal fuzzy coincidence points [15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”