This article is cited in 6 papers

Papers published in the English version of the journal

Coupled Fixed-Point Results for $T$-Contractions on Cone Metric Spaces with Applications

H. Rahimi^a, P. Vetro^b, G. Soleimani Rad<sup>a

a</sup> Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran
^b Dipartimento di Matematica e Informatica, Università degli Studi Palermo, Palermo, Italy

Abstract: The notion of coupled fixed point was introduced in 2006 by Bhaskar and Lakshmikantham. On the other hand, Filipović et al. [M. Filipović et al.,"Remarks on "Cone metric spaces and fixed-point theorems of $T$-Kannan and $T$-Chatterjea contractive mappings"," Math. Comput. Modelling 54, 1467–1472 (2011)] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper we prove some coupled fixed-point theorems for certain $T$-contractions and study the existence of solutions of a system of nonlinear integral equations using the results of our work. The results of this paper extend and generalize well-known comparable results in the literature.

Keywords: cone metric space, coupled fixed point, $T$-contraction, sequentially convergent, subsequentially convergent.

Received: 22.04.2013
Revised: 27.03.2015

Language: English

 English version: Mathematical Notes, 2015, 98:1, 158–167

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