Points For Mixed Monotone Operators Research Articles

Probabilistic $ (\omega, \gamma, \phi) $-contractions and coupled coincidence point results

<abstract><p>In this paper, we introduce the notion of probabilistic $ (\omega, \gamma, \phi) $-contraction and establish the existence coupled coincidence points for mixed monotone operators subjected to the introduced contraction in the framework of ordered Menger $ PM $-spaces with Had${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over z} }}$ić type $ t $-norm. As an application, a corresponding result in the setup of fuzzy metric space is also obtained.</p></abstract>

New Fixed Point Theorems and Application of Mixed Monotone Mappings in Partially Ordered Metric Spaces

We consider the existence of a coupled fixed point for mixed monotone mapping F:X×X→X satisfying a new contractive inequality which involves an altering distance function in partially ordered metric spaces. We also establish some uniqueness results for coupled fixed points, as well as the existence of fixed points of mixed monotone operators. The presented results generalize and develop some existing results. In addition to an example as well as an application, we establish some uniqueness results for a system of integral equations.

Fixed points of mixed monotone operators for existence and uniqueness of nonlinear fractional differential equations

In this paper we study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems by using new fixed point results of mixed monotone operators on cones.

Some new results for single-valued and multi-valued mixed monotone operators of Rhoades type

In (2008), Zhang proved the existence of fixed points of mixed monotone operators along with certain convexity and concavity conditions. In this paper, mixed monotone single-valued and multi-valued operators of Rhoades type are defined and two fixed point theorems are proved. MSC:47H10, 47H07.

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.

New Fixed Point Theorems of Mixed Monotone Operators and Applications to Singular Boundary Value Problems on Time Scales

Some new existence and uniqueness theorems of fixed points of mixed monotone operators are obtained, and then they are applied to a nonlinear singular second-order three-point boundary value problem on time scales. We prove the existence and uniqueness of a positive solution for the above problem which cannot be solved by using previously available methods.

Fixed point theorems of ϕ convex − ψ concave mixed monotone operators and applications

In this paper, ϕ convex − ψ concave mixed monotone operators are introduced and some new existence and uniqueness theorems of fixed points for mixed monotone operators with such convexity concavity are obtained. As an application, we give one example to illustrate our results.

Fixed point theorems for a class of mixed monotone operators with applications

In this paper we provide several unique existence theorems for fixed points for mixed monotone operators without continuity and compactness, and apply them to study a class of integral equations.

New existence and uniqueness theorems of positive fixed points for mixed monotone operators with perturbation

In this paper, we obtain some new and general existence and uniqueness theorems of positive fixed points for mixed monotone operators with perturbation, which extend the corresponding results in [Z.T. Zhang, New fixed point theorems of mixed monotone operators and applications, J. Math. Anal. Appl. 204 (1996) 307–319, Theorem 1, Corollaries 1 and 2]. Moreover, some applications to nonlinear integral equations on unbounded region are given.

Existence and uniqueness of fixed points for mixed monotone operators with applications

In this paper, we study the uniqueness and existence of fixed points of mixed monotone operators in the partially ordered Banach space. Our conclusions essentially improve the relevant results obtained by Liang and others. Moreover, as an application of our results, we prove the existence and uniqueness of a positive solution for a class of integral equations which cannot be solved by using previously available methods.

Fixed-point theorems of φ concave-(− ψ) convex mixed monotone operators and applications

In this paper, φ concave-(− ψ) convex operators are introduced and some new existence and uniqueness theorems of fixed points of mixed monotone operators with such concavity and convexity are obtained. Moreover, some applications to nonlinear integral equations on bounded or unbounded regions are given.

Existence of coupled quasi-fixed points for mixed monotone operators and its application to the discontinuous integral equations

Existence theorems of minimal and maximal coupled quasi-fixed points for the complex type mixed monotone operator in partial order topological spaces are established. As its application, we investigate the existence of the minimal and maximal coupled quasi-solution for the discontinuous Hammerstein integral equation in Banach space. Our results improve and extend some well-known results.

Iterative method for coupled quasi-solutions of mixed monotone operator equations

In this paper, we obtain some new existence theorems of the coupled quasi-fixed points for mixed monotone operators under more general conditions. Our results improve and extend many well-known results. Finally, we apply our results to Hammerstein integral equations.

Existence and uniqueness of positive fixed points for mixed monotone operators and applications

Some existence and uniqueness theorems of positive fixed points for mixed monotone operators are obtained and applications to initial value problems and two-point boundary value problems for ordinary differential equations are given.

Fixed points of mixed monotone operators with applications

Existence and uniqueness theorems of fixed points for some mixed monotone operators are investigated and applications to ordinary differential equations are given

Existence of multiple quasifixed points of mixed monotone operators by iterative techniques

Fixed point theorems of mixed monotone operators by iterative technique in a Banach space with the ordering relative to cone K. The notion of coupled quasi-fixed points is introduced and the main result shows their existence.