Manish Jain

Coupled Fixed Point Theorems for a Pair of Weakly Compatible Maps along with CLRg Property in Fuzzy Metric Spaces

The aim of this paper is to extend the notions of E.A. property and CLRg property for coupled mappings and use these notions to generalize the recent results of Xin-Qi Hu (2011). The main result is supported by a suitable example.

Coupled common fixed point results involving a ( φ , ψ ) -contractive condition for mixed g -monotone operators in partially ordered metric spaces

In the setting of partially ordered metric spaces, using the notion of compatible mappings, we establish the existence and uniqueness of coupled common fixed points involving a (φ,ψ)-contractive condition for mixed g-monotone operators. Our results extend and generalize the well-known results of Berinde (Nonlinear Anal. TMA 74:7347-7355, 2011; Nonlinear Anal. TMA 75:3218-3228, 2012) and weaken the contractive conditions involved in the results of Alotaibi et al. (Fixed Point Theory Appl. 2011:44, 2011), Bhaskar et al. (Nonlinear Anal. TMA 65:1379-1393, 2006), and Luong et al. (Nonlinear Anal. TMA 74:983-992, 2011). The effectiveness of the presented work is validated with the help of suitable examples.MSC:54H10, 54H25.

Coupled common fixed point results involving ( ϕ , ψ ) -contractions in ordered generalized metric spaces with application to integral equations

We establish some coupled coincidence and coupled common fixed point theorems for the mixed g-monotone mappings satisfying (ϕ,ψ)-contractive conditions in the setting of ordered generalized metric spaces. Presented theorems extend and generalize the very recent results of Choudhury and Maity (Math. Comput. Model. 54(1-2):73-79, 2011). To illustrate our results, an example and an application to integral equations have also been given.MSC:54H10, 54H25.

A Unique Coupled Common Fixed Point Theorem for Symmetric -Contractive Mappings in Ordered -Metric Spaces with Applications

We establish the existence and uniqueness of coupled common fixed point for symmetric -contractive mappings in the framework of ordered G-metric spaces. Present work extends, generalize, and enrich the recent results of Choudhury and Maity (2011), Nashine (2012), and Mohiuddine and Alotaibi (2012), thereby, weakening the involved contractive conditions. Our theoretical results are accompanied by suitable examples and an application to integral equations.

Coupled common fixed point results under new nonlinear contractions in ordered G-metric spaces

The present paper deals with the establishment of some coupled common fixed point results for mixed monotone operators satisfying new nonlinear contractions in ordered G-metric spaces. The mappings considered are commutative. Present study enrich as well as generalize the very recent works present in [15, 21, 22, 23, 24]. The work is furnished with suitable illustrations.

Coupled Fixed Point Theorems for ()-Contractive Mixed Monotone Mappings in Partially Ordered Metric Spaces and Applications

The object of this paper is to establish the existence and uniqueness of coupled fixed points under a ( , )-contractive condition for mixed monotone operators in the setup of partially ordered metric spaces. Presented work generalizes the recent results of Berinde (2011, 2012) and weakens the contractive conditions involved in the well-known results of Bhaskar and Lakshmikantham (2006), and Luong and Thuan (2011). The effectiveness of our work is validated with the help of a suitable example. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations.

A New Technique to Compute Coupled Coincidence Points

We compute coupled coincidence points without assuming the condition of compatibility of the pair of maps and relaxing the continuity condition of both the maps. In fact, our technique improves the technique introduced by Sintunavarat et al. (2011) which was then used by Hussain et al. (2012) to obtain coupled coincidence points.