Advanced Fixed Point Results in Generalized b-Metric Spaces: Theory and Application

Abstract

Fixed point theory has become a fundamental tool in nonlinear analysis, with wide-ranging applications in differential equations, optimization, and applied sciences. The classical Banach contraction principle provides a cornerstone for such studies; however, its strict assumptions limit broader applicability. This paper develops novel fixed point theorems in generalized b-metric spaces, extending the framework introduced. By introducing hybrid contraction conditions, the proposed results generalize several well-known principles introduced. Applications to nonlinear integral equations are also presented, demonstrating the practical relevance of the theoretical findings.