كتب fixed point theorems in b metric spaces
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Fixed Point Theorems in b- metric Spaces (كتاب)
This book presents a comprehensive study of fixed point theory within the framework of **b-metric spaces**, which generalize classical metric spaces by relaxing the triangle inequality. The work focuses on the existence, uniqueness, convergence, and stability of fixed points for both **single-valued and multivalued mappings** under various generalized contraction conditions.
The book begins with foundational concepts, introducing b-metric spaces, their topological properties, and essential preliminary results. It then reviews classical and modern fixed point theorems, including Banach, Kannan, Chatterjea, Reich, Hardy–Rogers, and **F-contractions**, highlighting how these results extend beyond standard metric spaces.
A major contribution of the book lies in developing **new fixed point theorems for generalized contractions** in complete b-metric spaces, including results for **non-expansive mappings**, **coincidence points**, and **multivalued mappings**. The author also investigates the **Ulam–Hyers stability** of fixed point problems and provides answers to previously open questions without relying on restrictive conditions such as proximinality.
Overall, the book advances metric fixed point theory by unifying and extending several contraction principles in b-metric spaces, offering results that are applicable to nonlinear analysis, differential equations, and other areas of mathematical research .
