In this paper, we obtain some sufficient conditions for the existence and uniqueness of point of coincidence by using simulation functions in the context of metric spaces and prove some interesting results. Our results generalize the corresponding results of [5, 8, 13, 14, 16] in several directions. Also, we provide an example which shows that our main result is a proper generalization of the result of Jungck [American Math. Monthly 83(1976) 261-263], L-de-Hierro et al. [J. Comput. Appl. Math 275(2015) 345-355] and of Olgun et al. [Turk. J. Math. (2016) 40:832-837].

In this paper, we introduced the concept of (α, β)-admissible Geraghty type contractive mappings. Sufficient conditions for the existence of a fixed point for such class of generalized nonlinear contractive mappings in metric spaces are provided. As applications, we derive a fixed point theorem for these contractions whenever the space is endowed with a graph. Some interesting consequences of our theorems are also obtained. The proved results generalize and extend various well-known results in the literature. Some examples are illustrated for the usability of the results.

In this paper, we obtain some fixed point results for generalized weakly contractive mappings with some auxiliary functions in the framework of b-metric spaces. The proved results generalize and extend the corresponding well-known results of the literature. Some examples are also provided in order to show that these results are more general than the well-known results existing in literature. MSC:47H10, 54H25.