We introduce the concept of a mixed g -monotone mapping and prove coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces. Presented theorems are generalizations of the recent fixed point theorems due to Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379–1393] and include several recent developments.

Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces

In this paper, we introduce a new concept of α – ψ -contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results.

Fixed point theorems for α–ψ-contractive type mappings

The purpose of this paper is to present some fixed point theorems for weakly contractive maps in a complete metric space endowed with a partial order.

Fixed point theorems for weakly contractive mappings in partially ordered sets

Fixed point theorems for generalized contractions in ordered metric spaces

We establish fixed point theorems for a new class of contractive mappings. As consequences of our main results, we obtain fixed point theorems on metric spaces endowed with a partial order and fixed point theorems for cyclic contractive mappings. Various examples are presented to illustrate our obtained results.

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Generalized - Contractive Type Mappings and Related Fixed Point Theorems with Applications

We present some fixed point results for monotone operators in a metric space endowed with a partial order using a weak generalized contraction-type assumption.

El Gebeily

Papers

Generalized contractions in partially ordered metric spaces