Abstract and Applied Analysis

New Existence Results and Generalizations for Coincidence Points and Fixed Points without Global Completeness

Wei-Shih Du

Full-text: Open access

Abstract

Some new existence theorems concerning approximate coincidence point property and approximate fixed point property for nonlinear maps in metric spaces without global completeness are established in this paper. By exploiting these results, we prove some new coincidence point and fixed point theorems which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, Kikkawa-Suzuki's fixed point theorem, and some well known results in the literature. Moreover, some applications of our results to the existence of coupled coincidence point and coupled fixed point are also presented.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 214230, 12 pages.

Dates
First available in Project Euclid: 18 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1366306767

Digital Object Identifier
doi:10.1155/2013/214230

Mathematical Reviews number (MathSciNet)
MR3035194

Zentralblatt MATH identifier
1267.54042

Citation

Du, Wei-Shih. New Existence Results and Generalizations for Coincidence Points and Fixed Points without Global Completeness. Abstr. Appl. Anal. 2013 (2013), Article ID 214230, 12 pages. doi:10.1155/2013/214230. https://projecteuclid.org/euclid.aaa/1366306767


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