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We prove some results on the existence and uniqueness of fixed points defined on a b-metric space endowed with an arbitrary binary relation. As applications, we obtain some statements on the coincidence of points involving a pair of mappings. Our results generalize, extend, modify and unify several well-known results and, especially, the results obtained by Alam and Imdad [J. Fixed Point Theory Appl., 17, 693–702 (2015); Fixed Point Theory, 18, 415–432 (2017), and Filomat, 31, 4421–4439 (2017)] and Berzig [J. Fixed Point Theory Appl., 12, 221–238 (2012)]. In addition, we provide an example to illustrate the suitability of the obtained results. [ABSTRACT FROM AUTHOR]

Some common fixed-point results for mappings satisfying a nonlinear weak contraction condition within the framework of ordered metric spaces are obtained. The accumulated results generalize and extend several comparable results well-known from the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish some coupled coincidence point theorems for mappings having a mixed g- monotone property in partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature. [ABSTRACT FROM AUTHOR]

Sufficient conditions for the existence of a common fixed point of R-subweakly commuting mappings are established within the framework of a convex metric space. As applications, we obtain various results on the best approximation for this class of mappings generalizing the results known from the literature. [ABSTRACT FROM AUTHOR]