1st Edition
Lights and Shadows on Generalizations in Fixed Point Theory
Fixed point theory is a powerful tool in nonlinear analysis, with applications in fractional differential equations and other areas. The most prominent application/ conclusion of this theory is the Banach contraction principal. Introduced for the first time, the notion of invisible graphs, will find applications in different areas of science, has been reviewed.
The book examines the classical techniques of this theory with a critical approach, along with the emergence of various generalizations in its evolution. Using the latest theories of the philosophy of science, the author aims to provide a philosophical explanation for the gaps in the fixed point theory and introduce the reader to profound mathematical-philosophical challenges.
Preface. Introduction. Orders, cones and graphs. Metric structures. Some modern fixed point results. Fixed point results for set-valued mappings. Some types of α-ψ-contractive set-valued mappings. Quasi-contractions and T-stability. Some false results on rate of convergence. Some false generalizations. References.
Biography
Prof Shahram Rezapour, He is full-professor of mathematics at Azarbaijan Shahid Madani University (Iran), and visiting professor position at China Medical University, Taichung, Taiwan. He had also eminent scholarship position at Kyung Hee University, Seoul, Republic of Korea in 2023. His name appeared in the list of Highly cited researchers in 2016 2017 and 2021. He has published more than 400 papers and some books during the years 2002-2024. His works are in different areas of Mathematics such Functional Analysis, Approximation Theory, Fixed Point Theory, Fractional Calculus, Finite Difference Equations, Numerical Analysis, Inclusion Problems, Bio-Mathematics and Modeling Theory.
