This book offers a comprehensive exploration of the Banach contraction principle and its many facets. A compilation of chapters authored by global experts, it is aimed at researchers and graduate students in mathematics. The content covers the Banach contraction principle, its generalizations, extensions, consequences and applications, focusing on both single-valued and multi-valued mappings across various spaces. While discussing theoretical foundations, this book uniquely emphasizes the practical applications of the Banach contraction principle in real-world problem-solving scenarios.

Each chapter addresses specific topics, including fractals, fractional differentials, integral equations, elastic beam problems and mathematical modeling and analysis of electrical circuits. These diverse subjects showcase the principle’s versatility in solving complex issues that go beyond theoretical mathematics. By highlighting Banach’s contraction principle as a lasting legacy, the book not only honours past mathematical achievements but also anticipates future innovations in industrial and applied mathematics. It underscores the enduring relevance of the principle, ensuring its continued prominence in mathematical discourse and its pivotal role in driving advancements across the field. This comprehensive exploration catalyzes inspiring future developments in mathematical research.