Summability, Fixed Point Theory and Generalized Integrals with Applications

This book presents contemporary mathematical concepts and techniques including theories of summability, fixed point and non-absolute integration and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results of double sequence spaces as the four-dimensional forward difference matrix in double sequence spaces, several new fixed point on Hadamard type fractional integral and differential operator related to the qualitative properties of solutions like, existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. It also includes several new areas of nonabsolute integration theory are introduced and their applications to other fields. This reference text is for researchers, academics, and professionals in the field of pure and applied mathematics.

• Covers recent research breakthroughs in this field offering new approaches and methods for both theoretical exploration and practical application
• Presents insights into functional analytic methods in summability, absolute and strong summability, direct theorems on summability, special and general summability methods, and their applications
• Highlights fixed-point theory’s application to real-world problems and offers solutions to various complex challenges
• Introduces new areas of non-absolute integration theory, such as the Henstock-Kurzweil integral and generalized Riemann integral
• Discusses sequence spaces and functional analysis, including the exploration of double sequence spaces and the four-dimensional forward difference matrix, offering valuable contributions to ongoing research

Dr. Hemanta Kalita is a Doctorate from Gauhati University. He has an academic experience of 13 years and has worked at various levels up to Assistant Professor. He has 36 publications in peer reviewed International journals with high impact factor and has 2 publications in various International Conferences held in India and abroad. Dr. Kalita has been an expert speaker in various International Conferences and has organized International Conference (ICNAA-2022), and International Conference (ICNACT-2024). Dr. Kalita was an Invited researcher at Usak University, Turkey, 2023. Dr. Kalita has published two issues in Journal of nonlinear and convex analysis as a guest editor in 2023 and 2024. He is working on Function spaces, integration theory, measure theory and generalized fractal calculus. Dr. Kalita has research collaborators in several countries of Europe, USA, Asian and Africa. Prof Dr. Talat Nazir is a Professor of Mathematics in Department of Mathematical Sciences, University of South Africa, South Africa. Prof Nazir obtained the PhD Degree of Mathematics in the research area of Nonlinear Analysis in in 2012. Then, he did two Post Doctorates of Mathematics, one from Netherlands in 2014 and other from Sweden in 2016. Prof Nazir is a famous researcher of Mathematics and have research collaboration with several international researchers worldwide. He published over hundred research articles, book chapters, and books in the peer reviewed international journals with high impact factors. Prof Nazir is also working on some research projects of Sciences, Engineering and Technology. He is a member of several international mathematical societies. He is also the editorial board member of several reputed journal of mathematics. He has also delivered several contributed talks at various international conferences and research seminars.

Dr. Mehmet Gurdal has served Suleyman Demirel University in the capacity of Lecturer to Full Professor since 1997. He received his PhD degree from Suleyman Demirel University, Isparta, Turkey. His main research interests are in the fields of sequence spaces, summability theory, mathematical analysis, Berezin symbol and operator theory. Within the framework of international France-Turkey cooperation, he completed a research stays at the University of Claude Bernard Lyon 1 in Lyon and carried out an international project. He has lectured nationally and internationally. He has participated as a reviewer for the American Mathematical Society. He has published one book, seven book chapter and more than 160 research papers in several reputed journals. He is a regular reviewer of many scientific journals and member of the editorial board of various scientific journals, international scientific bodies and organizing committees. He became a Governing Board-Advisory Board member of the scientific and technological research council of Turkey (TUBITAK). He was deemed worthy of many awards, especially the Turkish Academy of Sciences Outstanding Young Scientist award (GEBIP-2015). He has directed bachelor, master, and doctoral theses and has directed various research stays. https://scholar.google.com.tr/citations?user=U5y5eisAAAAJ &hl=tr

Dr. Sanket Tikare is an Assistant Professor in the Department of Mathematics, at Ramniranjan Jhunjhunwala College, Mumbai, India, which is an empowered autonomous college affiliated with the University of Mumbai, India. He did his M.Sc. and Ph.D. in Mathematics, both from Shivaji University, Kolhapur, India in the years 2008 and 2012 respectively. He is specialized in Applied Analysis. His research area of interest includes time scale theory, dynamic equations on time scales, differential equations, difference equations, fractional equations. He has published several research papers in international journals. He has collaborated with several eminent researchers from various institutes around the globe. He is member of a life member of the Indian Mathematical Society, a life member of the International Society of Difference Equations. Sanket Tikare is a regular reviewers of many highly-reputed international journals. Moreover, he has written reviews on several articles for Mathematical Reviews (AMS) and Zentralblatt Math (Germany). He has delivered invited talks at 20 international conferences. He has also delivered several contributed talks at various conferences in India and abroad.