Coincidence best proximity point of Fg -weak contractive mappings in partially ordered metric spaces

Abstract

The aim of this paper is to present coincidence best proximity point results of F g -weak contractive mappings in partially ordered metric space. Some examples are presented to prove the validity of our results.

C-class functions and pair (F,h) Upper class on common best proximity points results for new proximal C-contraction mappings

“…Now, we prove that {s n } is cauchy. By, (18) it is enough to show that subsequence {s 2n } is cauchy. Suppose, to the contrary, that {s 2n } is not a Cauchy sequence.By lemma (1.9) there exists >0 for which we can find subsequences {s 2n k }and {s 2m k } of {s 2n }with 2n k > 2m k > 2k such that…”

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“…In recent years, the idea of F-contraction has attracted the attention of several researchers and by now there exists a considerable literature on and around this concept (see [5][6][7][8][9][10][11][12][13][14][15][16][17][18] and references therein). Definition 1.4 A metric space (X, d) together with a partially order ''"'' on it is called ordered metric space and denoted by ðX; d; "Þ.…”

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“…Thus, a best proximity pair theorem furnishes sufficient conditions for the existence of an optimal approximate solution x, known as a best proximity point of the mapping F, satisfying the condition that d(x, Fx) = d(A, B). Many authors established the existence and convergence of fixed and best proximity points under certain contractive conditions in different metric spaces (see e.g., [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] and references therein).…”