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. The notion of invisible graphs, introduced here for the first time, will find applications in different areas of science.

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.

Prof Shahram Rezapour, is full professor of mathematics at Azarbaijan Shahid Madani University (Iran), and visiting professor at China Medical University, Taichung, Taiwan. He also had an eminent scholarship position at Kyung Hee University, Seoul, Republic of Korea in 2023. His name appeared on the list of Highly Cited Researchers in 2016, 2017 and 2021. He published more than 400 papers and some books during the years 2002-2024. His works are in different areas of mathematics including functional analysis, approximation theory, fixed point theory, fractional calculus, finite difference equations, numerical analysis, inclusion problems, biomathematics and modeling theory.