Results on Coincidence and Common Fixed Points for (ψ,φ)g-Generalized Weakly Contractive Mappings in Ordered Metric Spaces

Abstract

Inspired by a metrical-fixed point theorem from Choudhury et al. (Nonlinear Anal. 2011, 74, 2116-2126, we prove some order-theoretic results which generalize several core results of the existing literature, especially the two main results of Harjani and Sadarangani (Nonlinear Anal. 2009, 71, 3403-3410 and 2010, 72, 1188-1197. We demonstrate the realized improvement obtained in our results by using a suitable example. As an application, we also prove a result for mappings satisfying integral type (ψ, ϕ) g -generalized weakly contractive conditions.

Order-Theoretic Common Fixed Point Results in Rmb-Metric Spaces

“…Nieto and Rodriguez-Lopez [16,17] closely followed this paper. On such topics, there is currently a great deal of research effort underway, and one might look to these works (see [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]) and the papers cited therein.…”

Fixed point results for F-expansive mappings in ordered metric spaces

“…In 2004, Ran and Reurings [3] presented the analogous of Banach contraction principle in partially ordered metric spaces. Thereafter, proving order-theoretic analogues of metric-theoretical …xed point results becomes increasingly active (e.g., [4][5][6][7][8][9][10][11][12]). Concerning F -contractions in order metric spaces, one can be refereed to [13][14][15][16][17] and references therein.…”

An observation on $$\alpha$$ α -type F-contractions and some ordered-theoretic fixed point results

“…For the work of this kind, one can be referred to [24][25][26][27][28][29][30][31]. Abbas et al [32] utilized the idea of F-contraction to obtain order-theoretic common fixed point results.…”