Functional Equations and Stability Theory

Methods and Applications in Science and Engineering

Häftad, Engelska, 2027

AvAli Turab,Josue Antonio Nescolarde Selva,Andr�s Montoyo

2 369 kr

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Functional Equations and Stability Theory: Methods and Applications in Science and Engineering presents current advancements in the theory of functional equations and their stability, with a particular emphasis on their applications across science, engineering, and computational domains. Functional equations-long-standing pillars of mathematical analysis-have experienced a transformative evolution through the lens of Hyers-Ulam stability theory and its generalizations, which now intersect with key disciplines including artificial intelligence, cognitive science, and cybersecurity. This book provides readers with both principles of classical theory along with contemporary applications, thereby advancing the discourse on functional equations beyond its traditional confines. The book provides readers with both foundational studies and emerging methodologies, exploring how stability properties-such as Ulam-Hyers and generalized stability-are not only central to pure mathematics but also critically relevant to the modeling of real-world systems. By presenting methods that span theoretical results, fixed point methods, approximation techniques, and interdisciplinary case studies, this book offers a comprehensive perspective for readers interested in both mathematical rigor and real-world impact.

The book features chapters on advanced topics including classical and generalized stability of Cauchy, Jensen, Drygas, and Pexider-type equations; functional equations in restricted domains and abstract metric spaces; fixed point techniques for analyzing nonlinear and operatorial equations; stability in functional inequalities and mixed-type systems; applications to cognitive modeling, behavioral dynamics, and learning systems; functional frameworks in information theory, entropy, and communication systems; operator-valued and matrix functional equations; stability-informed modeling in cybersecurity, robotics, and intelligent environments; and, approximation and numerical approaches to stability problems. As such, the authors address both computational and mathematical dimensions, empowering readers to apply functional equations and stability theory to contemporary scientific problems.

Presents a systematic approach to the foundational mathematics and computational techniques of functional equations and stability theory, including classical theory along with contemporary interdisciplinary applications
Each chapter includes survey components, novel findings, and open research problems to encourage future investigation, along with executable program code and simulation files for worked examples
Presents advanced techniques such as classical and generalized stability of Cauchy, Jensen, Drygas, and Pexider-type equations
Covers functional equations in restricted domains and abstract metric spaces, fixed point techniques for analyzing nonlinear and operatorial equations, stability in functional inequalities and mixed-type systems, as well as operator-valued and matrix functional equations

Produktinformation

Utgivningsdatum2027-02-01
Mått191 x 235 x undefined mm
FormatHäftad
SpråkEngelska
Antal sidor250
FörlagElsevier Science
ISBN9780443515965

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Dr. Ali Turab is an Associate Professor at the School of Software, Northwestern Polytechnical University (NPU), China. He holds a Ph.D. in Applied Mathematics from Thammasat University, Thailand, where he also completed postdoctoral research in mathematical modeling and dynamical systems. His work integrates functional equations, stability theory, and machine learning to analyze decision-making, adaptive behavior, and cognitiveprocesses in both natural and engineered systems. With a background spanningtheoretical mathematics and computational applications, Dr. Turab has contributed to interdisciplinary domains including animal cognition, behavioral neuroscience, AI-driven modeling, and intelligent systems. His researchincorporates nonlinear analysis, cognitive neural networks, and fractional calculus in the study of complex systems. Dr. Turab has published widely in international journals and conferences, and actively supervises graduateresearch in mathematical modeling and artificial intelligence. He is committedto advancing the intersection of mathematics and behavioral sciences, and his work offers innovative perspectives on the application of functional equations and stability theory to real-world problems such as behavioral prediction, simulation, and computational cognition. Prof. Josué Antonio Nescolarde Selva is a Full Professor in the Department of Applied Mathematics at the University of Alicante, Spain. His research encompasses functional equations, biomathematics, cybernetics, data science, and the philosophy of science, with over 100 scientific publications indexed inhigh-impact journals. He has supervised several doctoral dissertations and ledcollaborative research with institutions across Europe, the U.S., and Asia. Prof. Nescolarde has served as Guest Editor-in-Chief for multiple special issues and is an editorial board member of JCR-indexed journals including Applied Artificial Intelligence and International Journal of General Systems. His expertise includes the application of functional equations to modeling biological systems, social dynamics, and intelligent decision-making frameworks. He has led or participated in numerous competitive R&D projects,both nationally and internationally, contributing to the mathematical underpinnings of complex system analysis. His leadership and academiccontributions continue to bridge abstract mathematical theory with practicalapplications across disciplines. Prof. Andrés Montoyo is a Full Professor in the Department of Software and Computing Systems at the University of Alicante, Spain, and a senior member of the GPLSI research group. His research focuses on natural languageprocessing, semantic modeling, and information extraction, with strong applications in intelligent systems and computational behavior analysis. He has authored over 80 papers in high-impact journals and over 100 conference papers, and has advised numerous doctoral theses in AI, language modeling,and knowledge systems. Prof. Montoyo has led or participated in over 75 funded R&D projects, including several EU and nationally competitive grants. His recent work explores the integration of functional modeling techniques withdeep learning for behavior-oriented applications, aligning closely with thethemes of this volume. He has also developed and transferred several software systems under intellectual property licenses and maintains an active role in technological dissemination and industry-academia collaboration. His academic leadership and interdisciplinary expertise bring critical insights to the intersection of mathematical theory, AI, and real-world behavioral systems.

1. Introduction: The Evolution of Functional Equations and Stability Theory2. Classical Stability Results: Hyers–Ulam and Its Generalizations3. Functional Equations on Restricted Domains and Metric Spaces4. Fixed Point Techniques in Functional and Operator Equations5. Stability of Functional Inequalities and Control-Oriented Models6. Behavioral Modeling via Functional Equations7. Applications in Information Theory and Entropy Measures8. Matrix and Operator-Valued Functional Equations9. Numerical Methods for Stability Problems10. Functional Equations in Cybersecurity and Cryptographic Systems11. Applications in Robotics, AI, and Learning Systems12. Functional Equations in Mathematical Biology and Epidemiology13. Recent Trends and Open Problems in Stability Theory14. Author Index and Contributor Biographies

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