New fixed point results under generalized $c$-distance in $tvs$-cone $b$-metric spaces with an application to systems of Fredholm integral equations

Abstract

In this paper, we define a generalized $c$-distance in $tvs$-cone$b$-metric spaces and introduce some results about its properties.Then we prove some new fixed point and common fixed point results(with the underlying cone which is not normal). Respective resultsconcerning mappings without periodic points are also deduced. Someexamples are presented to validate our obtained results. Anapplication to system of Fredholm integral equations is presented.