Open Access Research

Kannan-type contractions and fixed points in uniform spaces

Kazimierz Włodarczyk* and Robert Plebaniak

Author Affiliations

Department of Nonlinear Analysis, Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland

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Fixed Point Theory and Applications 2011, 2011:90  doi:10.1186/1687-1812-2011-90

Published: 30 November 2011

Abstract

In uniform spaces, using <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2011/1/90/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2011/1/90/mathml/M1">View MathML</a>-families of generalized pseudodistances, we construct four kinds of contractions of Kannan type and, by techniques based on these generalized pseudodistances, we prove fixed point theorems for such contractions. The results are new in uniform and locally convex spaces and even in metric spaces. Examples are given.

MSC: 47H10; 47H09; 54E15; 46A03; 54E35.

Keywords:
uniform space; metric space; <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2011/1/90/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2011/1/90/mathml/M1">View MathML</a>-family of generalized pseudodistances; contractions of Kannan type; fixed point; iterative approximation