We will investigate some existence, uniqueness, and Ulam-Hyers stability results for fixed point problems via --contractive mapping of type-() in the framework of -metric spaces. The presented theorems extend, generalize, and unify several results in the literature, involving the results of Samet et al. (2012).

The proofs of Theorems 2.1, 2.2 and 2.3 from [Olatinwo M.O., Some results on multi-valued weakly jungck mappings in b-metric space, Cent. Eur. J. Math., 2008, 6(4), 610–621] base on faulty evaluations. We give here correct but weaker versions of these theorems.

In this article, the authors introduced the concept of graphical fuzzy metric spaces which is a generalization of fuzzy metric spaces with the help of a relation. The authors discussed some topological structure, convergence criteria, and proved a Banach fixed-point result in graphical fuzzy metric space. As an application of obtained results, the authors find a solution of an integral equation and nonlinear fractional differential equations in the context of graphical fuzzy metric spaces. The authors provided some examples to illustrate the obtained results herein.

In this paper we give some common fixed point theorems for Ćirić type operators in complex valued b-metric spaces. Also, some corollaries under this contraction condition are obtained. Our results extend and generalize the results of Hammad et al. In the second part of the paper, in order to strengthen our main results, an illustrative example and some applications are given.

In this manuscript, some tripled fixed point results are presented in the framework of complete metric spaces. Furthermore, Wardowski’s contraction was mainly applied to discuss some theoretical results with and without a directed graph under suitable assertions. Moreover, some consequences and supportive examples are derived to strengthen the main results. In the last part of the paper, the obtained theoretical results are used to find a unique solution to a system of functional and integral equations.