Recently, Samet et al  introduced the concept of alpha-psi 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  and well known fixed point theorems due to Banach, Kannan, Chatterjea, Zamfirescu, Berinde, Suzuki, Ciric, Nieto, Lopez, and many others. We prove that alpha-psi 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; alpha-psi 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
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