Mixed G-monotone Property Research Articles

Mixed g-monotone property and quadruple fixed point theorems in partially ordered metric spaces

In this manuscript, we prove some quadruple coincidence and common fixed point theorems for F : X 4 ® X and g : X ® X satisfying generalized contractions in partially ordered metric spaces. Our results unify, generalize and complement various known results from the current literature. Also, an application to matrix equations is given. 2000 Mathematics subject Classifications: 46T99; 54H25; 47H10; 54E50.

Coupled coincidence points for mixed monotone operators in partially ordered metric spaces

In this paper, we give and prove some coupled coincidence point theorems for mappings F : X × X → X and g : X → X in partially ordered metric space X, where F has the mixed g-monotone property. Our results improve and generalize the results of Bhaskar and Lakshmikantham (Nonlinear Anal TMA 65:1379–1393, 2006), Luong and Thuan (Bull Math Anal Appl 2(4):16–24, 2010), Harjani et al. (Nonlinear Anal 74:1749–1760, 2011) and Choudhury et al. (Ann Univ Ferrara 57:1–16, 2011). We also give some examples to illustrate our results.

Coupled coincidences for multi-valued contractions in partially ordered metric spaces

AbstractIn this article, we study the existence of coupled coincidence points for multi-valued nonlinear contractions in partially ordered metric spaces. We do it from two different approaches, the first is Δ-symmetric property recently studied in Samet and Vetro (Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces, Nonlinear Anal. 74, 4260-4268 (2011)) and second one is mixed g-monotone property studied by Lakshmikantham and Ćirić (Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70, 4341-4349 (2009)).The theorems presented extend certain results due to Ćirić (Multi-valued nonlinear contraction mappings, Nonlinear Anal. 71, 2716-2723 (2009)), Samet and Vetro (Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces, Nonlinear Anal. 74, 4260-4268 (2011)) and many others. We support the results by establishing an illustrative example.2000 MSC: primary 06F30; 46B20; 47E10.

Coupled coincidence points for monotone operators in partially ordered metric spaces

Using the notion of compatible mappings in the setting of a partially ordered metric space, we prove the existence and uniqueness of coupled coincidence points involving a (ϕ, ψ)-contractive condition for a mappings having the mixed g-monotone property. We illustrate our results with the help of an example.

Coupled Random Fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces

Let (X, ≤) be a partially ordered set and suppose there is a metric d on X such that (X, d) is a complete separable metric space and (Ω, Σ) be a measurable space. In this article a pair of random mappings F: Ω × (X × X) → X and g: Ω × X → X, where F has a mixed g-monotone property on X, and F and g satisfy the non-linear contractive condition (5) below, are introduced and investigated. Two coupled random coincidence and coupled random fixed point theorems are proved. These results are random versions and extensions of recent results of Lakshmikantham and Ćirić [V. Lakshmikantham and Lj. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal.—Theor. 70(12) (2009): 4341–4349] and include several recent developments.