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- Title
SOME FIXED POINT THEOREMS FOR GENERALIZED α-GERAGHTY CONTRACTION TYPE MAPPINGS IN B-METRIC SPACES AND SOME APPLICATIONS TO THE NONLINEAR INTEGRAL EQUATION.
- Authors
Nguyen Trung Hieu; Le Thi Chac
- Abstract
The aim of this paper is to introduce the notion of a generalized α-Geraghty contraction type mapping in b-metric spaces and state the existence and uniqueness of a fixed point for this mapping. These results are generalizations of certain main results in [D. Dukiš, Z. Kadelburg, and S. Radenovic, Fixed points of Geraghty-type mappings in various generalized metric spaces, Abstr. Appl. Anal. 2011 (2011), 13 pages] and [O. Popescu, Some new fixed point theorems for α-Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl. 2014:190 (2014), 1 - 12]. Some examples are given to illustrate the obtained results and to show that these results are proper extensions of the existing ones. Then we apply the obtained theorem to study the existence of solutions to the nonlinear integral equation.
- Subjects
FIXED point theory; MATHEMATICAL mappings; NONLINEAR integral equations
- Publication
Facta Universitatis, Series: Mathematics & Informatics, 2017, Vol 32, Issue 2, p231
- ISSN
0352-9665
- Publication type
Article
- DOI
10.22190/FUMI1702231H