CONE b-METRIC-LIKE SPACES OVER BANACH ALGEBRA AND FIXED POINT THEOREMS WITH APPLICATION

The purpose of this article is to introduce a new generalization of the b-metric-like spaces called cone b-metric-like space over a Banach algebra A. Moreover, we discuss the topology generated by a cone b-metric-like space over Banach algebra . We also define generalized contraction mappings and expansive mappings in the new structure and prove some fixed point theorems for such mappings in the framework of cone b-metric-like space over Banach algebra. An example is also given to support the obtained results. Furthermore, we illustrate the application of our main results to the existence of solution of an integral equation. Our results extend, unify and generalize well known results of literature.