Fixed point theorems in extended $b$-suprametric spaces with applications

The primary objective of this study is to establish novel fixed point theorems for single-valued mappings satisfying generalized contraction conditions in the framework of extended $b$ -suprametric spaces. These results not only generalize and unify existing fixed point results in the literature but also provide a broader context for analysis. Building upon this foundation, we further derive corresponding fixed point theorems in suprametric and $b$-suprametric spaces as special cases of our main results. To highlight the relevance and originality of the proposed theorems, we present a concrete example that validates the applicability and sharpness of the key findings. Finally, we demonstrate the practical significance of our theoretical contributions by applying the main result to establish the existence of solutions for a nonlinear Volterra-Fredholm integral equation.