Extensions of Banach's fixed point theorem and applications


Marija Cvetković


University of Niš, Serbia


Tue, 21/02/2017 - 12:00pm to 1:00pm


RC-4082, The Red Centre, UNSW


Perov's theorem is one of many different extensions of the famous Banach fixed point theorem, one which is notable for its wide spectra of applications. It claims existence and uniqueness of a fixed point for a new class of contractive mappings. Russian mathematician A. I. Perov introduced a concept of generalized metric with values in $\mathbb{R}^n$ and defined a contractive condition that includes a matrix with nonnegative elements instead of a contractive constant.

We give extensions of this result in various settings and include different type of contractions. A contraction of Perov type on a cone metric space involves an operator instead of a matrix. Other extensions of Perov's theorem are inspired by quasi-contraction along with some results for common and coupled fixed point problems. We will discuss applications of the presented results in solving differential equations and Ulam-Hyers stability of functional equations.

 (This is joint work with Vladimir Rako\v cevi\'c)

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