‎In 1897‎, ‎Hensel introduced a normed space which does‎‎not have the Archimedean property‎. ‎During the last three decades‎‎theory of non--Archimedean spaces has gained the interest of‎‎physicists for their research in particular in problems coming‎‎from quantum physics‎, ‎p--adic strings and superstrings‎. ‎In this paper‎, ‎we prove‎‎the generalized Hyers--Ulam--Rassias stability for a‎‎system of additive‎, ‎quadratic and cubic functional equations in‎‎non--Archimedean normed spaces‎. Manuscript profile

In this paper, we apply the idea of integral type contraction and prove some coupled fixed point theorems for such contractions in ordered $G$-metric space. Also, we support the main results by an illustrative example. Manuscript profile

The main purpose of this article is to introduce the concept of $T$-contraction type mappings in the function weighed metric spaces and to obtain some coupled fixed points theorems in this framework. Also, an example and an application of the existence of a solution of a system of nonlinear integral equations are considered to protect the main results. Manuscript profile