Generalized contraction in b-metric spaces and Application to Nonlinear optimal control

Abstract

Fixed point theory plays a crucial role in addressing challenges in nonlinear
systems, particularly in the context of optimal control. The complexity of these systems
often complicates the establishment of solutions, especially when traditional methods
are applied in varying metric spaces. This paper presents a novel approach by utilizing
fixed point theorems specifically within b-metric spaces, offering effective solutions to
these challenges. By demonstrating the existence and uniqueness of fixed points in this
framework, we provide a pathway for ensuring convergence in optimal control strategies.
Ultimately, our findings underscore the significance of integrating fixed point theory with
b-metric spaces to enhance practical applications in nonlinear control