Some convergence theorems of a sequence in complete metric spaces and its applications.
In this paper we examine the set of weakly continuous solutions for a Volterra integral equation in Henstock-Kurzweil-Pettis integrability settings. Our result extends those obtained in several kinds of integrability settings. Besides, we prove some new fixed point theorems for function spaces relative to the weak topology which are basic in our considerations and comprise the theory of differential and integral equations in Banach spaces.
The aim of this paper is to introduce the concepts of compatible mappings and compatible mappings of type in non-Archimedean Menger probabilistic normed spaces and to study the existence problems of common fixed points for compatible mappings of type , also, we give an applications by using the main theorems.