Lights and Shadows on Generalizations in Fixed Point Theory

<p>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.</p><p>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.</p>