Open Access Research

Cyclic generalized contractions and fixed point results with applications to an integral equation

Hemant Kumar Nashine1, Wutiphol Sintunavarat2 and Poom Kumam2*

Author Affiliations

1 Department of Mathematics, Disha Institute of Management and Technology, Satya Vihar, Vidhansabha-Chandrakhuri Marg, Mandir Hasaud, Raipur, Chhattisgarh, 492101, India

2 Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, 10140, Thailand

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Fixed Point Theory and Applications 2012, 2012:217  doi:10.1186/1687-1812-2012-217

Published: 28 November 2012

Abstract

We set up a new variant of cyclic generalized contractive mappings for a map in a metric space and present existence and uniqueness results of fixed points for such mappings. Our results generalize or improve many existing fixed point theorems in the literature. To illustrate our results, we give some examples. At the same time as applications of the presented theorems, we prove an existence theorem for solutions of a class of nonlinear integral equations.

MSC: 47H10, 54H25.

Keywords:
fixed point; cyclic generalized <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2012/1/217/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2012/1/217/mathml/M1">View MathML</a>-contraction; integral equation