Employing Locally Finitely T-Transitive Binary Relations to Prove Coincidence Theorems for Nonlinear Contractions

In this article, we prove some relation-theoretic results on coincidence and common fixed point for a nonlinear contraction employing a locally finitely T-transitive binary relation, where T stands for a self-mapping on the underlying metric space. Our newly proved results deduce sharpened versions of certain relevant results of the existing literature. Finally, we adopt some examples to substantiate the genuineness of our proved results herein.

Some Common Coupled Fixed Point Theorems in Sb-Metric Spaces

In this paper, we prove some common coupled fixed point theorems for mapping satisfying a nonlinear contraction in Sb-metric space and some results are also given in the form of corollary. Also, some examples are given to verify the main results.

Fixed point theorems for nonlinear contractions with applications to iterated function systems

We introduce a new type of nonlinear contraction and present some fixed point results without using continuity or semi-continuity. Our result complement, extend and generalize a number of fixed point theorems including the the well-known Boyd and Wong theorem [On nonlinear contractions, Proc. Amer. Math. Soc. 20(1969)]. Also we discuss an application to iterated function systems.