Fixed Point Theorems in Convex b-Metric Spaces an‎d Applications

10/21/2025 12:00:00 AM

This dissertation, investigates an‎d develops fixed-point theorems in convex b-metric spaces. Fixed-point theory, as a powerful tool in mathematical analysis an‎d applied sciences, plays a fundamental role in solving differential an‎d integral equations. In this research, we first review the basic concepts of fixed-point theorems in ordinary metric spaces. Then, by introducing generalized spaces such as b-metric spaces an‎d convex metric spaces, the classical theorems are extended to these structures. The main focus of this study is on presenting an‎d proving new fixed-point theorems for various mappings in convex b-metric spaces, which encompass both the generalized properties of b-metric spaces an‎d convex spaces. Finally, the practical applications of these theorems in solving a class of integral equations are discussed to demonstrate the effectiveness an‎d importance of the theoretical results obtained. The findings of this research can serve as a theoretical foundation for future studies in fields related to nonlinear analysis an‎d solving equations.

نقطه ثابت , فضاي متريك , فضاي -bمتريك , فضاي متريك محدب , فضاي -bمتريك محدب , قضيه باناخ , معادلات انتگرال

Fixed Point , Metric Space , b-Metric Space , Convex Metric Space , Convex b-Metric Space , Banach’s Theorem , Integral Equations

Majid Mansourzadeh

Dr. Mohammad Bagher Ghaemi