The existing literature of fixed point theory contains many results enunciating fixed point theorems for self-mappings in metric and Banach spaces. Recently, Huang and Zhang [4] introduced the concept of cone metric spaces which generalized the concept of the metric spaces, replacing the set of real numbers by an ordered Banach space, and obtained some fixed point theorems for mapping satisfyin...

Abstract In this paper, the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced. The fixed point theorems satisfying contractive conditions are obtained, without appealing to completeness of X or normality cone. continuity mapping relaxed. Furthermore, we prove that necessary if has a . These results greatly generalize several well-known comparable liter...

In this paper, we introduce the concepts of an inferior idempotent cone and a BID-cone b-metric space over Banach algebra. We establish some new existence theorems fixed point in setting complete spaces Some fundamental questions examples are also given.

In this research, we first check that the abstract cone b -metric is discontinuous in case of normal by a counter example. We obtain several meaningful results about generalized id="M3"> -quasicontraction and Ćirić-type id="M4"> id="M5"> spaces over Banach algebras, weakening certain important conditions mappings. Meanwh...