Nguyen Van Luong

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.

Coupled fixed point theorems in partially ordered G-metric spaces

Abstract In this paper, we prove some coupled fixed point theorems for nonlinear contractive mappings having the mixed monotone property in partially ordered G -metric spaces. The results on fixed point theorems are generalizations of the recent results of Choudhury and Maity [B.S. Choudhury, P. Maity, Coupled fixed point results in generalized metric spaces, Math. Comput. Modelling 54 (2011) 73–79].

Coupled fixed point theorems for mixed monotone mappings and an application to integral equations

In this paper, we extend the coupled fixed point theorems for a mixed monotone mapping F:XxX->X in partially ordered metric spaces established by Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379-1393]. An application to nonlinear integral equations is also given to illustrate our results.

Coupled points in ordered generalized metric spaces and application to integro-dierential equations

Abstract In this paper, we prove some coupled fixed point theorems for O-compatible mappings in partially ordered generalized metric spaces under certain conditions to extend and complement the recent fixed point theorems due to Bhaskar and Lakshmikantham [Nonlinear Anal. TMA 65 (2006) 1379 - 1393] and Berinde [Nonlinear Anal. TMA 74 (2011) 7347-7355]. We give some examples to illustrate our results. An application to integro-differential equations is also given.

Coupled Coincidence Point Theorem in Partially Ordered Metric Spaces via Implicit Relation

We prove a coupled coincidence point theorem for mappings F : 𝑋×𝑋→𝑋 and g : 𝑋→𝑋, where F has the mixed g-monotone property, in partially ordered metric spaces via implicit relations. Our result extends and improves several results in the literature. Examples are also given to illustrate our work.

Fixed point theorem for generalized weak contractions satisfying rational expressions in ordered metric spaces

In this paper, we prove a fixed point theorem for generalized weak contractions satisfying rational expressions in partially ordered metric spaces. The result is a generalization of a recent result of Harjani et al. (Abstr. Appl. Anal, Vol.2010, 1-8, 2010). An example is also given to show that our result is a proper generalization of the existing one.2000 Mathematics Subject Classification: 47H10, 54H25.

A unique common coupled fixed point theorem for four maps under Ψ-Φ contractive condition in partial metric spaces

In this paper, we obtain a unique coupled common fixed point theorem for four maps in partial metric spaces.