On Fixed Point of Quasi Contraction with Application to Integral Equation

It is observed from the surveyed literature that there is no sufficient study of quasi-weakly contractive operators in the context of b-metric-like spaces. From this background information, this paper introduces a new unified notion of the quasi-weakly contractive operator in b-metric-like space. It examines the existence and uniqueness of invariant points of such operators. The idea put forward herewith subsumes a few known results in the literature. Non-trivial illustrations are constructed to verify our proposed concepts and to compare them with other corresponding ones. Corollaries which reduce our findings to other famous ideas are presented and discussed. As an application, one of our obtained corollaries is utilised to investigate new existence criteria for solving a class of boundary value problem.

Keywords:

Fixed point , b-metric-like , Integral equation