Geodesic
Fixed points for \(\alpha\)-\(\psi\) contractive mappings with an application to quadratic integral equations
Electronic journal of differential equations, Tome 2014 (2014)
Recently, Samet et al [24] 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 [24] 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.
Classification : 47H10, 54E50, 34A12, 34A30, 34D20
Keywords: metric space, alpha-psi contraction, fixed point, quadratic integral equation 
@article{EJDE_2014__2014__a24,
     author = {Samet,  Bessem},
     title = {Fixed points for \(\alpha\)-\(\psi\) contractive mappings with an application to quadratic integral equations},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1315.54043},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a24/}
}
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Samet,  Bessem. Fixed points for \(\alpha\)-\(\psi\) contractive mappings with an application to quadratic integral equations. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a24/