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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.
List of contents
Common fixed point for pairs of Weakly compatible mappings using F-contraction.- Coincidence points of mappings on relational metric Spaces with applications.- Some fixed point result in m-metric space using different contractions.- Application of common fixed point in the framework of b-metric space via simulation function.- Relation-theoretic fixed point results in extended Rectangular mr -metric spaces.- Julia fractals of complex-valued cosine functions via fixed point iterations.- Some fixed-circle results with mix-type contractions on metric spaces.- Application of fixed point iterations in generation of fractals for higher-order complex polynomial.- Rational type fixed-disc and common fixed-disc results on metric and s-metric spaces via Geraghty type contractions.- Coupled Fixed Points in Ordered Fuzzy Metric Spaces and an Elastic Beam Problem.- Data Dependence, Stability and Convergence Rate of Novel Iterative Algorithm.- A New Generalization of Metric Space and Banach Contraction Principle.- Trajectory and Exact Controllability results on Impulsive Nonlocal Differential System with Deviated Argument.- Banach contraction in Altering JS-metric space to decipher aggregate voltage of electric circuit.- Common fixed point for families of weakly subsequentially continuous mappings.
