# Extensions of Banach's fixed point theorem and applications

Marija Cvetković

## Affiliation:

University of Niš, Serbia

## Date:

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

## Venue:

RC-4082, The Red Centre, UNSW

## Abstract:

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)