Abstract
Through this work, we analyze the structure of extended G(b) -metric spaces and show a fundamental lemma for sequence convergence within the same metric. We also propose the new notion of generalized geraghty type Theta-berinde contraction mappings and demonstrate several fixed point theorems for these mappings in the sense of extended G(b)-metric spaces. Eventually, the existence result for solutions of a Fredholm integral equation is furnished to show the efficacy of the technique developed.