Functional Equations and Stability Theory

Methods and Applications in Science and Engineering
Erscheinungsjahr 2027
ISBN: 978-0-443-51596-5
Verlag: Elsevier Science & Technology

Buch, Englisch, Format (B × H): 191 mm x 235 mm

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.

Autoren/Hrsg.

Turab, Ali

Selva, Josue Antonio Nescolarde

Montoyo, Andrés

Fachgebiete

• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Automatische Datenerfassung, Datenanalyse
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Software Engineering
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
• Mathematik | Informatik EDV | Informatik Informatik Mensch-Maschine-Interaktion Informationsarchitektur

Inhaltsverzeichnis

1. Introduction: The Evolution of Functional Equations and Stability Theory
2. Classical Stability Results: Hyers–Ulam and Its Generalizations
3. Functional Equations on Restricted Domains and Metric Spaces
4. Fixed Point Techniques in Functional and Operator Equations
5. Stability of Functional Inequalities and Control-Oriented Models
6. Behavioral Modeling via Functional Equations
7. Applications in Information Theory and Entropy Measures
8. Matrix and Operator-Valued Functional Equations
9. Numerical Methods for Stability Problems
10. Functional Equations in Cybersecurity and Cryptographic Systems
11. Applications in Robotics, AI, and Learning Systems
12. Functional Equations in Mathematical Biology and Epidemiology
13. Recent Trends and Open Problems in Stability Theory
14. Author Index and Contributor Biographies

Über Autor(innen)

Montoyo, Andrés
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 language
processing, 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 with
deep learning for behavior-oriented applications, aligning closely with the
themes 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.

Turab, Ali
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 cognitive
processes in both natural and engineered systems. With a background spanning
theoretical mathematics and computational applications, Dr. Turab has contributed to interdisciplinary domains including animal cognition, behavioral neuroscience, AI-driven modeling, and intelligent systems. His research
incorporates 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 graduate
research in mathematical modeling and artificial intelligence. He is committed
to 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.

Selva, Josue Antonio Nescolarde
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 in
high-impact journals. He has supervised several doctoral dissertations and led
collaborative 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 academic
contributions continue to bridge abstract mathematical theory with practical
applications across disciplines.