| Summary: | In this paper, we introduce the structure of extended cone <i>b</i>-metric-like spaces over Banach algebra as a generalization of cone <i>b</i>-metric-like spaces over Banach algebra. In this generalized space we define the notion of generalized Lipschitz mappings in the setup of extended cone <i>b</i>-metric-like spaces over Banach algebra and investigated some fixed point results. We also provide examples to illustrate the results presented herein. Finally, as an application of our main result, we examine the existence and uniqueness of solution for a Fredholm integral equation.
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