FIXED POINT THEOREMS IN EXTENDED COMPLEX PARTIAL b-METRIC SPACES WITH APPLICATIONS TO INTEGRAL EQUATIONS

Abstract

This paper introduces the notion of extended complex partial b-metric spaces,which unifies and extends several existing frameworks in the literature. Within this setting,we establish new common fixed point theorems for weakly increasing mappings of rationaltype, thereby generalizing a variety of known results from complex valued, partial, and b-metric spaces. To highlight the applicability of our theoretical contributions, we demonstratehow the proposed results can be applied to prove the existence and uniqueness of solutionsto systems of Urysohn integral equations and Caputo-type fractional differential equations.These applications illustrate not only the novelty but also the versatility of the developedframework. The results presented in this work provide new perspectives for xed point theoryin complex settings and open potential avenues for further research in functional analysisand applied mathematics.