Advanced Mathematical Analysis and Its Applications

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

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.