On Some Fixed‐Point Results in Cone <i>A</i> _<i>b</i> ‐Metric Space Over a Real Banach Algebra Without the Assumption of Normality of Cone

In this paper, we introduce the concept of cone A b ‐metric space over real Banach algebra and prove some fixed‐point theorems of the Banach, Chatterjea, and Kannan types in such space without assuming normality of the cone. Our results extend and generalize many previously known results in the existing literature. An example is given to support our results. We also apply our result to examine the existence of unique solution for a nonlinear Fredholm integral equation.