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.