1st Edition

Advanced Mathematical Analysis and its Applications

Edited By Pradip Debnath, Delfim F. M. Torres, Yeol Je Cho Copyright 2023
    492 Pages 35 B/W Illustrations
    by Chapman & Hall

    492 Pages 35 B/W Illustrations
    by Chapman & Hall

    Advanced Mathematical Analysis and its Applications presents state-of-the-art developments in mathematical analysis through new and original contributions and surveys, with a particular emphasis on applications in engineering and mathematical sciences. New research directions are indicated in each of the chapters, and while this book is meant primarily for graduate students, there is content that will be equally useful and stimulating for faculty and researchers.

    The readers of this book will require minimum knowledge of real, complex, and functional analysis, and topology.


    • Suitable as a reference for graduate students, researchers, and faculty
    • Contains the most up-to-date developments at the time of writing.

    Chapter 1. Generalized Boyd-Wong type Contractions
    Pradip Debnath

    Chapter 2. Remarks on the Metatheorem
    Sehie Park

    Chapter 3. On Wardowski Type Results within G-Metric Spaces
    Jelena Vujakovic, Slobodanka Mitrovic, Zoran Mitrovic, Stojan Radenovic

    Chapter 4. Some New Fixed-Point Results in Archimedean Type Intuitionistic Fuzzy B-Metric Space
    Nabanita Konwar

    Chapter 5. Fixed point Theorems for Quasi Upper Semicontinuous Set-Valued Mappings in p-Vector Spaces
    Shin-sen Chang, Yeol Je Cho, Sehie Park, George Xianzhi Yuan

    Chapter 6. Proinov E_S-contraction Type Unique and Non-Unique Fixed-Point Results on S-metric Spaces
    Nihal Tas

    Chapter 7. η_A-admissible Mappings for Four Maps in C*-algebra-valued MP-metric Spaces with an Application
    Samira Hadi Bonab, Vahid Parvaneh, Zohreh Bagheri

    Chapter 8. Summarized Proofs to Find Common Fixed Points of Presic Contractions for Four Maps
    Samira Hadi Bonab, Vahid Parvaneh, Zohreh Bagheri

    Chapter 9. Fixed Point Method: Ulam Stability of Mixed Type Functional Equation in β-Banach Modules
    K. Tamilvanan, N. Revathi, S. A. Mohiuddine

    Chapter 10. Hybrid Steepest Descent Methods for Solving Variational Inequalities with Fixed Point Constraints in a Hilbert Space: An Annotated Bibliography
    Mootta Prangprakhom, Nimit Nimana

    Chapter 11. Generalized Kannan Maps with Application to Iterated Function System
    B. V. Prithvi, S. K. Katiyar

    Chapter 12. Stability Analysis of Lotka-Volterra Models: Continuous, Discrete, and Fractional
    Sandra Vaz, Delfim F. M. Torres

    Chapter 13. Existence and Uniqueness of Solutions to Proper Fractional Riemann-Liouville Initial Value Problems on Time Scales
    Nedjoua Zine, Benaoumeur Bayour, Delfim F. M. Torres

    Chapter 14. Ostrowski type Inequalities for Conformable Fractional Calculus via a Parameter
    Miguel Vivas-Cortez, Seth Kermausuor, Juan E. Napoles Valdes

    Chapter 15. The Regional Observability Problem for a Class of Semilinear Time-Fractional Systems with with Riemann-Liouville Derivative
    Zguaid Khalid, El Alaoui Fatima-Zahrae

    Chapter 16. Construction of Fractional Extended Nabla Operator and Strong Convergence Analysis
    Leila Khitri-Kazi-Tani, Hacen Dib

    Chapter 17. Stability Analysis of Fractional Nonlinear Dynamical Systems
    Priyadharsini Sivaraj

    Chapter 18. On Periodic Dirichlet Series and Special Functions
    Jay Mehta, Imre Katai, Shigeru Kanemitsu

    Chapter 19. The Lotka-Volterra Dynamical System and its Discretization
    Marcia Lemos-Silva, Delfim F. M. Torres

    Chapter 20. A New Inertial Projection Algorithm for Solving Pseudomonotone Equilibrium Problems
    Tran Van Thang, Le Dung Muu

    Chapter 21. Convergence Analysis of a Relaxed Inertial Alternating Minimization Algorithm with Applications
    Yuchao Tang, Yang Yang, Jigen Peng

    Chapter 22. Ball Convergence of Iterative Methods without Derivatives with or without Memory Relying on the Weight Operator Technique
    Ioannis K. Argyros, Santhosh George, Christopher Argyros

    Chapter 23. Inner Product Generalized Trapezoid type Inequalities in Hilbert Spaces
    Silvestru Sever Dragomir

    Chapter 24. A Note on Degenerate Gamma Random Variables
    Taekyun Kim, Dae San Kim, Jongkyum Kwon, Hyunseok Lee

    Chapter 25. Dynamical Systems on Free Random Variables followed by the Semicircular Law
    Ilwoo Cho




    Pradip Debnath is an Assistant Professor (in Mathematics) at the Department of Applied Science and Humanities, Assam University, India. He earned his Ph.D. in Mathematics from the National Institute of Technology Silchar, India. His research interests include fixed point theory, nonlinear functional analysis, soft computing and mathematical statistics.

    He has published more than 60 papers in various journals of international repute and is an active reviewer for more than 50 international journals. He is also a reviewer for Mathematical Reviews published by the American Mathematical Society. He is the Lead Editor of the books Metric Fixed Point Theory - Applications in Science, Engineering and Behavioural Sciences (Springer Nature, 2021), Soft Computing Techniques in Engineering, Health, Mathematical and Social Sciences (CRC Press, 2021), Fixed Point Theory and Fractional Calculus: Recent Advances and Applications (Springer Nature, 2022), Soft Computing: Recent Advances and Applications in Engineering and Mathematical Sciences (CRC Press, 2023) and Advances in Number Theory and Applied Analysis (World Scientific, 2023). He is a topical advisory panel member of the journals “Axioms” and “Fractal and Fractional” and guest editor of several special issues for different journals.

    He has successfully guided Ph.D. students in the areas of nonlinear analysis, soft computing and fixed point theory. He has recently completed a major Basic Science Research Project in fixed point theory funded by the UGC, the Government of India. Having been an academic gold medalist during his post-graduation studies from Assam University, Silchar, Dr. Debnath has qualified several national-level examinations in mathematics in India.

    Delfim Fernando Marado Torres is a Portuguese Mathematician born 16 August 1971 in Mozambique. He obtained a PhD in Mathematics from the University of Aveiro (UA) in 2002, and habilitation in Mathematics, UA, in 2011. He is a full professor of mathematics since 9 March 2015. He has been the Director of the R&D Unit CIDMA, the largest Portuguese research center for mathematics, and Coordinator of its Systems and Control Group. His main research areas are calculus of variations and optimal control; optimization; fractional derivatives and integrals; dynamic equations on time scales; and mathematical biology.

    Torres has written outstanding scientific and pedagogical publications. In particular, he is author of two books with Imperial College Press; three books with Springer; and editor of several other books. Professor Torres has been recognized four times as one of the top 1% of Mathematicians on the prestigious global Clarivate Web of Science list and is the only Portuguese mathematician to be so honored. He has strong experience in graduate and post-graduate student supervision and teaching in mathematics. Twenty four PhD theses in mathematics have successfully been finished under his supervision. Moreover, he has been the leading member in several national and international R&D projects, including EU projects and networks. Professor Torres has been, since 2013, the Director of the Doctoral Programme Consortium in Mathematics and Applications (MAP-PDMA) of Universities of Minho, Aveiro, and Porto.

    Delfim married in 2003 and has one daughter and two sons.

    Yeol Je Cho is Emeritus Professor at the Department of Mathematics Education, Gyeongsang National University, Jinju, Korea, and Distinguished Professor at the School of Mathematical Sciences, the University of Electronic Science and Technology of China, Chengdu, Sichuan, China. In 1984, he received his Ph.D. in Mathematics from Pusan National University, Pusan, Korea. He is a fellow of the Korean Academy of Science and Technology, Seoul, Korea, since 2006, and a member of several mathematical societies. He has organized international conferences on nonlinear functional analysis and applications, fixed point theory and applications and workshops and symposiums on nonlinear analysis and applications.

    He has published over 400 papers, 20 monographs and 12 books with renowned publishers from around the world. His research areas are nonlinear analysis and applications, especially fixed point theory and applications, some kinds of nonlinear problems, that is, equilibrium problems, variational inequality problems, saddle point problems, optimization problems, inequality theory and applications, stability of functional equations and applications. He has delivered several invited talks at international conferences on nonlinear analysis and applications and is on the editorial boards of 10 international journals of mathematics.