Mixed Monotone Property Research Articles

3-Dimensional computational analysis of [formula omitted]-contraction in GV-fuzzy metric spaces with applications

It is a well known fact that contraction conditions play a major role in composing coincidence point results. In present work, a new ϕ-contraction is being corroborated to yield coupled coincidence points in partially ordered GV-fuzzy metric spaces. Due to the significant feature of H-type t-norm, in this communication, we endue GV-fuzzy metric spaces with this t-norm. We use the mixed monotone property of mappings with regard to partial ordering. Present work generalizes some already existing results. An applied example is also formulated to cast the 3-dimensional analysis of ϕ-contraction utilized in the main result. Computational analysis of the illustrative example has been done using the software MATLAB version R2022b which shows the experimental verification of our work. Furthermore, applications to the solution of the system of Fredholm type integral equations and solution of the system of equations in dynamic programming accords the validity of the present work. Endmost, the concluding remark projects the significance of current work.

Bhaskar-Lakshmikantham fixed point theorem vs Ran-Reunrings one and some possible generalizations and applications in matrix equations

<p>We provided a generalization of the existence and uniqueness of fixed points in partially ordered metric spaces for a monotone map. We applied the major results in the investigation of coupled fixed points for ordered pairs of two maps that met various monotone features, which included a mixed monotone property or a total monotone property. To ascertain necessary requirements for the existence and uniqueness of solutions to systems of matrix equations, the results regarding coupled fixed points for ordered pairs of maps were utilized. These results are illustrated with numerical examples. Some of the known results are a consequence of the results we obtained.</p>

RELATION-THEORETIC COUPLED FIXED POINT THEOREMS

In this paper, we introduce mixed R-monotone property of a mapping and utilize the same to investigate existence and uniqueness of coupled fixed points in a metric space endowed with a binary relation R. Moreover, we present some coupled fixed point results for mappings without mixed monotone property using relation-theoretic approach. Our results generalize some well-known coupled fixed points theorems. Further, we give some illustrative examples in support of our results.

A new contribution in fuzzy cone metric spaces by strong fixed point techniques with supportive application

In this manuscript, the concept of a cyclic tripled type fuzzy cone contraction mapping in the setting of fuzzy cone metric spaces is introduced. Also, some theoretical results concerned with tripled fixed points are given without a mixed monotone property in the mentioned space. Moreover, under this concept, some strong tripled fixed point results are obtained. Ultimately, to support the theoretical results non-trivial examples are listed and the existence of a unique solution to a system of integral equations is presented as an application.

Coincidence of Fixed Points with Mixed Monotone Property

The purpose of this paper is to introduce and prove some coupled coincidence fixed point theorems for self mappings satisfying -contractive condition with rational expressions on complete partially ordered metric spaces involving altering distance functions with mixed monotone property of the mapping. Our results improve and unify a multitude of coupled fixed point theorems and generalize some recent results in partially ordered metric space. An example is given to show the validity of our main result.

Coupled coincidence points for hybrid pair of mappings via mixed monotone property in bipolar metric spaces

In this paper, we establish a coupled coincidence fixed point results for a hybrid pair of single valued and multivalued mappings satisfying generalized contractive conditions, defined on a partially ordered bipolar metric space. Our results unify, generalize and complement several known comparable results from the current literature. An example is given.

On Some Coupled Fixed Point Theorems with Rational Expressions in Partially Ordered Metric Spaces

The aim of this paper is to prove some coupled fixed point theorems of a self mapping satisfying a certain rational type contraction along with strict mixed monotone property in an ordered metric space. Further, a result is presented for the uniqueness of a coupled fixed point under an order relation in a space. These results generalize and extend known existing results in the literature.

Coupled fixed point analysis in fuzzy cone metric spaces with an application to nonlinear integral equations

In this paper, we introduce the concept of coupled type and cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. We establish some coupled fixed point results without the mixed monotone property, and also present some coupled fixed results using the partial order metric in the said space. We present some strong coupled fixed point theorems using cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. Moreover, we present an application of nonlinear integral equations for the existence of a unique solution to support our work.

Generalized Contractions to Coupled Fixed Point Theorems in Partially Ordered Metric Spaces

The purpose of this paper is to establish some coupled fixed point theorems for a self mapping satisfying certain rational type contractions along with strict mixed monotone property in a metric space endowed with partial order. Also, we have given the result of existence and uniqueness of a coupled fixed point for the mapping. This result generalize and extend several well known results in the literature

Coupled coincidence point results for mappings without mixed monotone property in partially ordered `G`-metric spaces

In this paper, we prove some coupled fixed point theorems for nonlinear contractive mappings which doesn't have the mixed monotone property, in the context of partially ordered `G`-metric spaces. Hence, these results can be applied in a much wider class of problems. Our results improve the result of D. Dori'{c}, Z. Kadelburg and S. Radenovi'{c} [Appl. Math. Lett. (2012)]. We also present two examples to support these new results.

Related Results to Hybrid Pair of Mappings and Applications in Bipolar Metric Spaces

In this paper, we introduce the concept of multivalued contraction mappings in partially ordered bipolar metric spaces and establish the existence of unique coupled fixed point results for multivalued contractive mapping by using mixed monotone property in partially ordered bipolar metric spaces. Some interesting consequences of our results are obtained.

A variational principle and coupled fixed points

We generalize Ekeland’s variational principle in partially ordered complete metric spaces on sets defined by functions with the mixed monotone property. We apply the result in giving an alternative proofs for coupled fixed points for mixed monotone maps in partially ordered complete metric spaces by using a variational technique. We succeed in generalizing some of the known results about coupled fixed points.

The new approach for some coupled fixed point results

The aim of this paper is to stand for new approach of the results of Jain et al. and Berinde. The proofs of all our results are without mixed monotone property. An example are also given to confirm the effectiveness of the presented work.

Fixed Point Theorems for Mappings Satisfying Weak Nonexpansivity Condition (Weak Contractivity Condition) into (from) Cartesian Products Normed Spaces

This paper suggests new types of weak nonexpansive mappings defined from normed space X into its Cartesian product X × X, studies the main features of the fixed points for those mappings and extends the concept of (C)-contractivity condition introduced in some previous research papers. On other side, it introduces new types of contraction mappings with a mixed monotone property; the {a, b, c} M-first type and the {a, b, c} M-second type contractions, these types are defined from the Cartesian product space X × X into X, where X is a sequentially ordered Banach space, proves the existence of first-anti-second and second-anti-first couple fixed points of such types and generalizes some of the results given before.

Fixed point theorems for a pair of single-valued operators in a metric space endowed with a reflexive relation

In this paper we provide some existence and uniqueness theorems for coupled fixed points for a pair of contractive operators satisfying a mixed monotone property, in a metric space endowed with a reflexive relation. An application to a first-order differential system equation with PBV conditions is also given to illustrate the utility of our results.

Unified multi-tupled fixed point theorems involving mixed monotone property in ordered metric spaces

In this chapter, we introduce a generalized notion of monotone property and prove some results regarding existence and uniqueness of multi-tupled fixed points for nonlinear contraction mappings satisfying monotone property in ordered complete metric spaces. Our results unify several classical and well-known n-tupled (including coupled, tripled and quadruple ones) fixed point results in the existing literature.

A Tripled Fixed Point Theorem in Partially Ordered Complete S-Metric Space

Sedghiet al.(Mat. Vesn. 64(3):258-266, 2012) introduced the notion of anS-metric as a generalized metric in 3-tuples S:X3→[0,∞), whereXis a nonempty set. In this paper we prove a tripled fixed point theorem for mapping having the mixed monotone property in partially ordered S-metric space. Our result generalize the result of Savitri and Nawneet Hooda (Int. J. Pure Appl. Sci. Technol. 20(1):111-116, 2014, On tripled fixed point theorem in partially ordered metric space) into the settings of S-metric space.

Coupled coincidence point in ordered cone metric spaces with examples in game theory

In this paper, we prove some coupled coincidence point theorems for mappings with the mixed monotone property and obtain the uniqueness of this coincidence point. Then we providing useful examples in Nash equilibrium.

Common Fixed Point Results for Generalized Symmetric Meir-Keeler Contraction

We introduce the concept of generalized weakly compatibility for the pair {F,G} of mappings F,G:X×X→X and also introduce the concept of common fixed point of the mappings F,G:X×X→X. We establish a common fixed point theorem for generalized weakly compatible pair of mappings F,G:X×X→X without mixed monotone property of any mapping under generalized symmetric Meir-Keeler contraction on a non complete metric space, which is not partially ordered. An example supporting to our result has also been cited. We improve, extend and generalize several known results.

TRIPLE FIXED POINT THEOREMS FOR MAPPINGS SATISFYING WEAK CONTRACTIONS UNDER F-INVARIANT SET

The aim of this paper to extend the results of the coupled fixed point theorems of Poom et. al. (2012) to triple fixed point theorems by weaking the concept of the mixed monotone property. The main results extend and unify the results of Poom et. al. and many results of the triple fixed point theorems. AMS Subject Classification: 47H10, 54H25