Generalized Contractions and Fixed Point Theorems

Approximate fixed point theorems for Geraghty-contractions

The purpose of this paper is to obtain necessary and suffcient conditionsfor existence approximate fixed point on Geraghty-contraction. In this paper,denitions of approximate -pair fixed point for two maps Tα , Sα and theirdiameters are given in a metric space.

Some Fixed Point Theorems for Generalized Contractions in Metric Spaces with a Graph

Jachymski [ Proc. Amer. Math. Soc., 136 (2008), 1359-1373] gave modified version of a Banach fixed point theorem on a metric space endowed with a graph. In the present paper, (G, Φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. Also, Hardy-Rogers G-contraction have been introduced and some fixed point theorems have been proved. S...

Fixed point theorems of JS-quasi-contractions

*Correspondence: [email protected] 3Department of Mathematics, Jiangxi University of Finance and Economics, Nanchang, 330013, China Full list of author information is available at the end of the article Abstract In this paper, we introduce the concept of JS-quasi-contraction and prove some fixed point results for JS-quasi-contractions in complete metric spaces under the assumption that the ...

Quadruple fixed point theorems for nonlinear contractions

The notion of coupled fixed point is introduced by Gnana-Bhaskar and Lakshmikantham. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut. In this manuscript, a quadruple fixed point is considered and some new related fixed point theorems are obtained. We also give some examples to illustrate our results. © 2012 Elsevier Ltd. All rights reserved.

Coupled Fixed Point Theorems under Weak Contractions