Darbo's Fixed Point Theory

This book serves as both a foundational text on Darbo's fixed point theorem and a practical guide for its application in functional analysis. It combines rigorous theoretical discussions with structured proofs, illustrative examples, definitions, and open-ended research directions. Fixed point theory is essential in both pure and applied mathematics, providing tools to solve equations, model equilibria, and analyze dynamical systems. However, many operators encountered in real applications - especially in partial differential equations (PDEs), integral equations, fractional integral equations, and control theory - are neither compact nor contractions. Darbo's theorem addresses this issue by relaxing the requirement of compactness to a weaker, yet effective concept. This makes the book a valuable resource for advanced students, researchers, analysts, and applied mathematicians alike.