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In this work we deal with set-valued functions with values in the power set of a separated locally convex space where a nontrivial pointed convex cone induces a partial order relation. A set-valued function is evenly convex if its epigraph is an evenly convex set, i.e., it is the intersection of an arbitrary family of open half-spaces. In this paper we characterize evenly convex set-valued functions as the pointwise supremum of its set-valued e-affine minorants. Moreover, a suitable conjugation pattern will be developed for these functions, as well as the counterpart of the biconjugation Fenchel-Moreau theorem. [ABSTRACT FROM AUTHOR]

Abstract This paper continues the study of the Axiom of Infinite Choice on transversal ordered spring spaces in terms of fixed point and increasing inductive sets. These principles unify a number of diverse results (about three thousand papers) in fixed point theory, especially recently published. Applications in partially ordered spaces and fixed point theory are also considered.

Using a one-parameter case as an example, we demonstrate that multicanonical simulations allow for accurate estimates of the residual combinatorial entropy of partially ordered ice. For the considered case, corrections to an (approximate) analytical formula are found to be small, never exceeding 0.5%. The method allows one as well to calculate combinatorial entropies for other systems. [ABSTRACT FROM AUTHOR]

In this paper, we study the mapping satisfying mixed g-monotone property in partially ordered complete Menger probabilistic G-metric spaces. By weakening the notion of Ψ, we prove some new coupled coincidence point theorems and coupled common fixed point theorems. Finally, we provide an example to illustrate our results. [ABSTRACT FROM AUTHOR]

New fixed point and coupled fixed point theorems in partially ordered ν-generalized metric spaces are presented. Since the product of two ν-generalized metric spaces is not in general a ν-generalized metric space, a different approach is needed than in the case of standard metric spaces. [ABSTRACT FROM AUTHOR]

New generalized forms of Banach and Kannan type contractions have been described and some coupled coincidence and coupled common fixed point results have been established in the setting of metric space involving a graph. Our theorems extend and generalize many existing results in the literature. Furthermore, an application to integral equations is presented to affirm the importance. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show the existence of best proximity points for multivalued Suzuki-Edelstein-Wardowski type α-proximal contractions in the setting of complete metric spaces and partially ordered metric spaces. We give examples to illustrate the main results. Our results improve and extend the corresponding results in the literature. [ABSTRACT FROM AUTHOR]

If L and M are partially ordered vector spaces, then one can consider regular linear maps from L to M, i.e. linear maps which can be written as the difference of two positive linear maps. If the space L is directed, then the space Lr(L,M) of all regular linear operators becomes a partially ordered vector space itself. We will mainly concern ourselves with the questions when the space Lr(L,M) is itself a Riesz space and how, even if it is not a Riesz space, its lattice operations work. The so-called Riesz-Kantorovich theorem gives sufficient conditions for which Lr(L,M) is a Riesz space and it also specifies the lattice operations by means of the Riesz-Kantorovich formula: if S,T∈Lr(L,M) and x∈L with x≥0 then the supremum S∨T in the point x is given by (S∨T)(x)=supS(y)+T(x-y):0≤y≤x.It is still an open problem if whenever in a more general setting the supremum of two regular operators exists in Lr(L,M), it automatically is given by the Riesz-Kantorovich formula. Our main result concerns the special case where L is a partially ordered vector space with a strong order unit and M is a (possibly infinite) product of copies of the real line, equipped with the lexicographic ordering. It will turn out that under some mild continuity and regularity conditions the lattice operations on Lr(L,M) are indeed given by the Riesz-Kantorovich formula, even though the space Lr(L,M) is not necessarily a Riesz space. [ABSTRACT FROM AUTHOR]

It is known since the late 1960's that the dual of the category of compact Hausdorff spaces and continuous maps is a variety - not finitary, but bounded by N1. In this note we show that the dual of the category of partially ordered compact spaces and monotone continuous maps is an N1-ary quasivariety, and describe partially its algebraic theory. Based on this description, we extend these results to categories of Vietoris coalgebras and homomorphisms on ordered compact spaces. We also characterise the N1-copresentable partially ordered compact spaces. [ABSTRACT FROM AUTHOR]

In this manuscript, using generalized type contraction, multi-valued coupled fixed point results in the set up of partially ordered metric space are studied. For the validity of the derived result appropriate example and application are also provided. [ABSTRACT FROM AUTHOR]

The notion of coincidence point and common fixed point were extended in generalized partially ordered fuzzy metric spaces. Under some conditions, some coincidence point and common fixed point theorems were established in generalized partially fuzzy metric spaces using weakly compatible mappings. These results improve some theorems in corresponding literature. [ABSTRACT FROM AUTHOR]

In this paper, we use the concept of Ab-metric space which is obtained by generalizing the definitions of A-metric space and b-metrc space. Using this concept, we prove some coupled fixed point theorems in partially ordered Ab-metric space. Examples are also presented to verify the obtained results. [ABSTRACT FROM AUTHOR]

We present some existence and convergence results for monotone α-nonexpansive mappings in partially ordered hyperbolic metric spaces. A recent result of Bin Dehaish and Khamsi [Browder and Göhde fixed point theorem for monotone nonexpansive mappings, Fixed Point Theory Appl. 2016, 2016:20] is complemented. [ABSTRACT FROM AUTHOR]

We present a general framework in which sub-supersolution techniques can be applied. Specifically, we consider a normed vector space endowed with a partial order. This allows us to introduce a notion of sub- and supersolutions relative to an equation driven by operators defined from the space to its topological dual. We provide sufficient conditions to guarantee that the interval determined by an ordered pair of sub-supersolutions contains a solution of the initial problem. We also study existence of extremal positive or negative solutions and location of nodal solutions. Examples of applications to quasilinear boundary value problems are given. [ABSTRACT FROM AUTHOR]

Double perovskite oxides A2BB'O6 combining 3d and 4d or 5d transition metal ions at the B and B' sites feature a variety of magnetic and magneto-electric properties. Targeting Ba2FeOsO6, we synthesized powder samples of nonstoichiometric Ba2Fe1.12Os0.88O6 by solid-state reaction from the oxides. The crystal structure was investigated by using synchrotron powder X-ray and powder neutron diffraction. In contrast to Ca2FeOsO6 and Sr2FeOsO6, the compound adopts the hexagonal 6L perovskite structure (space group P3m1) with partial Fe-Os order at both the face-sharing B2O9 dimer and the corner sharing BO6 transition metal sites. Magnetization, neutron diffraction, and 57Fe Mössbauer spectroscopy results show that Ba2Fe1.12Os0.88O6 develops ferrimagnetic order well above room temperature at TC ≈ 370 K. The nonsaturated magnetization curve at 2 K features a magnetic moment of 0.4 μB per formula unit at 7 T and a pronounced hysteresis with a coercive field of about 2 T. Large exchange bias effects are observed when the magnetization curves are measured after field cooling. The peculiar magnetic properties of Ba2Fe1.12Os0.88O6 are attributed to an inhomogeneous magnetic state formed as a consequence of the atomic disorder. Our results indicate that hexagonal double-perovskite-related oxides are a promising class of compounds for finding new materials with potential applications as hard magnets or in the area of spintronics. [ABSTRACT FROM AUTHOR]

In the paper the concept of covering (regularity) for set-valued mappings in partially ordered spaces is introduced. The coincidence points problem for set-valued mappings in partially ordered spaces is considered. Sufficient conditions for the existence of coincidence points of isotone and orderly covering set-valued mappings are obtained. It is shown that the known theorems on coincidence points of covering and Lipschitz mappings in metric spaces can be deduced from the obtained results. [ABSTRACT FROM AUTHOR]

In this article, without using the notion of compatible mappings, we prove the existence and uniqueness of coupled coincidence points for mixed gmonotone mappings in the setting of partially ordered metric spaces, these results improve and generalize some well-known results in the literature. [ABSTRACT FROM AUTHOR]

The aim of the paper is to introduce new Suzuki and convex type contractions and prove new best proximity results for these contractions in the setting of a metric space. As applications, we deduce similar results for such type of contractions in partially ordered metric spaces and derive new Suzuki type fixed point results. An illustrative example is provided here to highlight our findings. [ABSTRACT FROM AUTHOR]

Under some weaker conditions, some coincidence point and common fixed point theorems are established in partially ordered fuzzy metric spaces using weakly compatible mappings. By using the theorems, we obtain some coupled and multidimensional fixed point results, which are generalization and improvement of very recent theorems in the corresponding literature. In order to illustrate our main results, we give three examples. [ABSTRACT FROM AUTHOR]

We obtain sufficient conditions for the existence and uniqueness of best proximity points for a new class of non-self mappings involving simulation functions in a metric space endowed with a partial order. Some interesting consequences including fixed point results via simulation functions are presented. [ABSTRACT FROM AUTHOR]

In this paper, we proved some common fixed point theorems of mappings satisfying almost generalized contractive condition in complete partially ordered G-metric spaces. These results extend, unify and generalize several well-known corresponding results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish some fixed point theorems with T-contractions and w-distances in partially ordered metric spaces. The main tool used in our proof is a generalized altering distance function. Our results can be applied directly to study multidimensional fixed point which covers the concepts of coupled, tripled, quadruple fixed point etc. Moreover, a Fredholm integral equation and an initial-value problem for partial differential equation of parabolic type are also discussed. [ABSTRACT FROM AUTHOR]

In this paper we establish some best proximity point results using generalized weak contractions with discontinuous control functions. The theorems are established in metric spaces with a partial order. We view the main problem in the paper as a problem of finding an optimal approximate solution of a fixed point equation. We also discuss several corollaries and give an illustrative example. We apply our result to obtain some coupled best proximity point results. [ABSTRACT FROM AUTHOR]

For multifactor experimental designs in which the levels of at least one of the factors are ordered we show how to construct components that provide a deep nonparametric scrutiny of the data. The components assess generalised correlations and the resulting tests include and extend the Page and umbrella tests. Application of the tests described is straightforward. Orthonormal polynomials on the ANOVA responses and the factors are required and the formulae needed are given subsequently. These depend on the moments of the responses and of each factor and are easily calculated. Products of at least two of these orthonormal polynomials are then used as inputs into standard ANOVA routines. For example, using the first order orthonormal polynomial on factor A and the second order orthonormal polynomial on the ANOVA response will assess if, with increasing levels of factor A there is an umbrella response with either an increase and then a decrease or a decrease and then an increase. [ABSTRACT FROM AUTHOR]

The aim of this article is to present, improve and generalize some recent coincidence and coupled coincidence point results from several papers in the framework of partially ordered b-metric spaces. Two examples are also provided to support the superiority of the obtained results. [ABSTRACT FROM AUTHOR]

We consider properties of convex directed subgroups for the interpolation groups in which each element is a quotient of two almost orthogonal elements. A series of results on values for almost orthogonal elements in those groups is obtained. We investigate characteristics of lexicographic extensions for partially ordered groups in which each element is a quotient of two almost orthogonal elements. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish random coincidence point results for weakly increasing random operators in the setting of ordered metric spaces by using generalized altering distance functions. Our results present random versions and extensions of some well-known results in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of cyclic weakly (ψ, ...)-contractive mappings and cyclic weakly (C, ψ, φ)-contractive mappings, and prove some fixed point theorems for such two types of mappings in complete partially ordered Menger PM-spaces. Some new results are obtained, which extend and generalize some fixed point results in metric and probabilistic metric spaces. Some examples are given to support our results. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of coincidence points for nonlinear mappings of any number of arguments under a weak (ψ,φ) -contractive condition. Our results generalize, extend and unify several classical and very recent related results in the literature (see Aydi et al. (2011), Berinde (2010), Gnana-Bhaskar and Lakshmikantham (2006), Berzig and Samet (2012), Borcut and Berinde (2012), Choudhury et al. (2011), Karapınar and Luong (2012), Lakshmikantham and Ćirić (2009), Luong and Thuan (2011), Roldán (2012)). [ABSTRACT FROM AUTHOR]

The concept of covering (regularity) for mappings in partially ordered spaces is introduced. Sufficient conditions for the existence of coincidence points and minimal coincidence points of isotone and orderly covering mappings are obtained. These results generalize classical fixed point theorems for isotone mappings. Moreover, the known theorems on coincidence points of covering and Lipschitz mappings in metric spaces are deduced from the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of w--compatibility and weakly commutativity for the hybrid pair of mappings F : X4 → 2X and g : X → X and establish a quadruple fixed point theorem for multivalued mapping under φ -- ψ contraction in the context of partially ordered metric spaces. As an application of the first theorem, we obtain a quadruple coincidence and common quadruple fixed point for hybrid pair of mappings. We also give examples to illustrate our results. We also improve and generalize several known results. [ABSTRACT FROM AUTHOR]

An n-tuplet fixed point is a generalization of the well-known concept of "coupled fixed point and tripled fixed point". The intent of this paper is to introduce the concept of mixed strict monotone property and generalize Meir-Keeler contraction for mapping F: Xn → X, where n is an arbitrary positive integer. Also establish an n-tuplet fixed point theorem for mappings F: Xn → X under a generalized Meir-Keeler contraction in the setting of partially ordered metric spaces. Related examples are also given to support our main results. Our results are the generalizations of the results of B. Samet[8] and Hassen et al. [15]. Also as application, some results of integral type are given. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we have used a method of reducing tripled coincidence and tripled fixed point results in (ordered) metric spaces to the respective results for mappings with one variable, even obtaining (in some cases) more general theorems. Our results generalize, extend, unify, enrich and complement recently tripled coincidence point theorems established by Berinde and Borcut (2011) [4], Borcut and Berinde (2012) [7] and Borcut (2012) [9]. Also, by using our method several coupled coincidence and coupled common fixed point results in ordered metric spaces can be reduced to the coincidence and common fixed point results with one variable. [Copyright &y& Elsevier]

The critical properties of classical frustrated helimagnets with different numbers of chiral order parameters are studied in three dimensions. The model of an antiferromagnet on a simple cubic lattice is considered with additional competing exchange interactions between spins of the first and the third range orders. In this model, helicoidal ordered phases exist with one, two, and three independent chiral order parameters. In all cases, it was found that a transition from an ordered to a disordered phase is a single first-order transition in the absence of partially ordered phases. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish some coupled coincidence point theorems for mappings having a mixed g- monotone property in partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature. [ABSTRACT FROM AUTHOR]

The concept of ordered g-contraction is introduced, and some fixed and common fixed point theorems for g-nondecreasing ordered g-contraction mapping in partially ordered metric spaces are proved. We also show the uniqueness of the common fixed point in the case of an ordered g-contraction mapping. The theorems presented are generalizations of very recent fixed point theorems due to Golubović et al. (Fixed Point Theory Appl. 2012:20, 2012). [ABSTRACT FROM AUTHOR]

In the setting of partially ordered metric spaces, we introduce the notion of generalized symmetric g-Meir-Keeler type contractions and use the notion to establish the existence and uniqueness of coupled common fixed points. Our notion extends the notion of generalized symmetric Meir-Keeler contractions given by Berinde et. al. [V. Berinde, and M. Pacurar, Coupled fixed point theorems for generalized symmetric Meir-Keeler contractions in ordered metric spaces, Fixed Point Theory and Appl., 2012, 2012:115, doi:10.1186/1687-1812-2012-115] to a pair of mappings. We also give some applications of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we prove a tripled fixed point theorem for the mapping having the mixed monotone property in partially ordered metric space. We also give an example in support of our result. [ABSTRACT FROM AUTHOR]

The article presents a mathematical study which examines the presence of coincidence points of mappings in the case of partially ordered spaces. The study discusses the standard concepts of partially ordered spaces, the definition of the mapping called monotone, and the conditions given for the problem. Details on the theorems used to satisfy the conditions mentioned in the study are provided.

In this paper, we introduce the concept of a $$w^{*}$$ -compatible mappings to obtain coupled coincidence point and coupled common fixed points of nonlinear contractive mappings in partially ordered metric spaces. Our results generalize, extend, unify, enrich and complement various comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

Abstract: Coupled fixed point problems have attracted much attention in recent times. In this paper we establish coupled coincidence point and coupled fixed point results in the context of fuzzy metric spaces. The two mappings considered here are assumed to be compatible. Hadžić type t-norm is used. By an application of the coincidence point theorem in fuzzy metric spaces, a corresponding result is obtained in metric spaces. The main theorem of this paper is illustrated with an example. Our work extends some existing results. [Copyright &y& Elsevier]

In this article we study the structure of solution sets within a special class of generalized Stampacchia-type vector variational inequalities, defined by means of a bifunction which takes values in a partially ordered Euclidean space. It is shown that, similar to multicriteria optimization problems, under appropriate convexity assumptions, the (weak) solutions of these vector variational inequalities can be recovered by solving a family of weighted scalar variational inequalities. Consequently, it is deduced that the set of weak solutions can be decomposed into the union of the sets of strong solutions of all variational inequalities obtained from the original one by selecting certain components of the bifunction which governs it. [ABSTRACT FROM AUTHOR]

In this manuscript, we prove new coupled fixed point theorems in the context of partially ordered partial metric spaces. The main theorems of this paper extent by improving some earlier results in the literature. We also present applications of these new results through a number of examples. [ABSTRACT FROM AUTHOR]