Contractivity of Leader type and fixed points in uniform spaces with generalized pseudodistances

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:387

Article

Wlodarczyk, Kazimierz¹  Plebaniak, Robert¹ 

[1] Univ Lodz, Dept Nonlinear Anal, Fac Math & Comp Sci, PL-90238 Lodz, Poland

关键词: Fixed point;    Contraction of Leader type;    Uniform space;    Locally convex space;    Metric space;    Generalized pseudodistance;   

DOI  :  10.1016/j.jmaa.2011.09.006

来源: Elsevier

【 摘 要 】

Recently, Jachymski and Jozwik proved that among various classes of contractions which are introduced and studied in the metric fixed point theory, the Leader contractions are greatest general contractions. In this article, we want to show how generalized pseudodistances in uniform spaces can be used to obtain new and general results of Leader type without complete graph assumptions about maps and without sequentially complete assumptions about spaces, which was not done in the previous publications on this subject. The definitions, results and methods presented here are new for maps in uniform and locally convex spaces and even in metric spaces. Examples showing a difference between our results and the well-known ones are given. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free