Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 152, pp. 118.
Fixed points for alphapsi contractive mappings with
an application to quadratic integral equations
Bessem Samet
Abstract:
Recently, Samet et al [24] introduced the concept of
alphapsi contractive mappings and studied the existence of
fixed points for such mappings. In this article, we prove three
fixed point theorems for this class of operators in complete metric spaces.
Our results extend the results in [24] and well known fixed point
theorems due to Banach, Kannan, Chatterjea, Zamfirescu, Berinde, Suzuki,
Ciric, Nieto, Lopez, and many others.
We prove that alphapsi contractions unify large classes of contractive
type operators, whose fixed points can be obtained by means of the
Picard iteration. Finally, we utilize our results to discuss the existence
and uniqueness of solutions to a class of quadratic integral equations.
Submitted May 10, 2014. Published June 30, 2014.
Math Subject Classifications: 47H10, 54E50, 34A12, 34A30, 34D20.
Key Words: Metric space; alphapsi contraction;
fixed point; quadratic integral equation.
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Bessem Samet
College of Science, King Saud University
Department of Mathematics
P.O. Box 2455, Riyadh 11451, Saudi Arabia
email: bsamet@ksu.edu.sa

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