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Rectangular metric space was first defined by Branciari [3] in 2000. In this paper we prove some fixed point theorems on vector valued rectangular metric space. Our results generalize some fixed point results for scalar valued. [ABSTRACT FROM AUTHOR]

S-metric space was introduced by Sedghi et al. [5] in 2012. We derive some common fixed point results for self-mappings on vector valued complete S-metric space. In support of our results, we also give some examples. [ABSTRACT FROM AUTHOR]

We introduce and study the framework of compact metric structures and their associated notions of isomorphisms such as homeomorphic and bi-Lipschitz isomorphism. This is subsequently applied to model various classification problems in analysis such as isomorphism of C*-algebras and affine homeomorphism of Choquet simplices, where among other things we provide a simple proof of the completeness of the isomorphism relation of separable, simple, nuclear C*-algebras recently established by M. Sabok. [ABSTRACT FROM AUTHOR]

Under the time-variable Dirichlet condition, the time-fractional diffusion equation with heat absorption in a sphere is taken into consideration. The time-fractional derivative with the power-law kernel is used in the generalized Cattaneo constitutive equation of the thermal flux. The Laplace transform and a suitable transformation of the independent variable and function are used to determine the analytical solution of the problem in the Laplace domain. To obtain the temperature distribution in the real domain, the inverse Laplace transforms of two functions of exponential type are obtained. These formulae are new in the literature. The particular cases of the classical Cattaneo law of heat conduction and of the classical Fourier's law are obtained from the solutions corresponding to the time-fractional generalized Cattaneo law. [ABSTRACT FROM AUTHOR]

In this paper, we give a complete description of Riesz spaces where every positive increasing and bounded from above sequence converges relatively uniformly. A Riesz space with this property will be called a Dedekind u-complete Riesz space. The location of this concept in the main inclusion theorem of Luxemburg and Zaanen will be investigated. [ABSTRACT FROM AUTHOR]

Let E be a Banach lattice and let S and T be operators defined on E such that 0 ≤ S ≤ T. We provide conditions under which S is a Riesz operator if T is a R iesz operator. [ABSTRACT FROM AUTHOR]

Quasinilpotent equivalent elements of a unital Banach algebra have the same left and right spectrum; if the Banach algebra is the algebra of operators on a Banach space, then they (also) have the same approximate point and subjectivity spectrum. We apply the notion of quasinilpotent equivalent to investigate perturbation of left/right and upper/lower Fredholm (and Weyl, Browder) spectrum by polynomially Riesz operators. The resulting theorems lead to an improvement of some recently obtained results. [ABSTRACT FROM AUTHOR]

In this paper we describe n-Banach lattices by Riesz space equipped with n-norm. We consider spaces of reguler operators and order bounded operators between n-Banach lattices and Banach lattices, we generate norm on these space by the aid of n-norm. Then we investigate properties of operators on these space with generated norm. [ABSTRACT FROM AUTHOR]

Frames by integer translates were studied by Kim and Kwon [6]. Christensen et.al [3] studied Riesz sequences of translates and their generalized duals. In this paper we consider a system of modulates for L²(ℝ). A necessary and sufficient condition for a system of modulates for L²(ℝ) to be a frame sequence (Riesz sequence, orthonormal sequence) is given. We also prove a result related to the frame operator of a frame sequence {EkΦ} k∈ℤ. Finally, it is proved that for n ≥ 1, the system of modulates {EkBn} k∈ℤ is a Riesz Fischer sequence. [ABSTRACT FROM AUTHOR]

To preserve the spatial consistency of low-level features, generalized Riesz-wavelet transform (GRWT) is adopted for fusing multi-modality images. The proposed method can capture the directional image structure arbitrarily by exploiting a suitable parameterization fusion model and additional structural information. Its fusion patterns are controlled by a heuristic fusion model based on image phase and coherence features. It can explore and keep the structural information efficiently and consistently. A performance analysis of the proposed method applied to real-world images demonstrates that it is competitive with the state-of-art fusion methods, especially in combining structural information. [ABSTRACT FROM AUTHOR]

• A mathematical model assuming prey refuge is a function of predator's density and hiding level of prey has been analyzed. • A time delay accounts for hiding behaviour of prey has been introduced, the delay parameter destabilizes the system. • Impact of fractional order, i.e., memory phenomenon has been explored in terms of stability analysis of the model system. • The probable biological explanations behind each obtained result of the model system have been thoroughly discussed. Most of the preys are well aware of sensing predation risk. Consequently, to escape from predators they usually adopt several defense mechanisms, specially refuge themselves to become invulnerable. In view of this, a mathematical model has been formulated incorporating prey refuge, where it is assumed that prey refuge is a function of predators availability in the system. It is shown that the model system is well-posed. It has been found that the hiding level and consumption rate of predators have a suitable interrelation between them. Both the parameters act as Hopf bifurcation parameters, but they play opposite role in case of stabilization of the system dynamics. Also, hiding level plays crucial role in maintaining the mean density of both the populations. Furthermore, as hiding behaviour of prey is not instantaneous, so a time delay, namely hiding delay has been introduced to make the model system more realistic and it is observed that the delay parameter destabilizes the system. Modelling approach through fractional calculus has been further deployed to study how the process of forgetting life history influences the dynamical intricacy of the population level dynamics. All the analytical findings have been testified by proper numerical performances. [ABSTRACT FROM AUTHOR]

In this note we prove a new result concerning absolute summability factor of an infinite series via quasi-f-power increasing sequence, improving some conditions used by Bor [2] and Leindler [4] in recent results. In fact we are giving two improvements to the result of Leindler. [ABSTRACT FROM AUTHOR]

Abstract: This paper is mainly concerned with the structure of the centre of a vector lattice. A special attention is paid in the case when , . In this paper we give some characterizations of dense vector sublattices of the centre. Those characterizations will be applied in several directions. At the end of this work we compare various fullness and richness properties of the centre of a vector lattice. [Copyright &y& Elsevier]

The variational principle and the differential equations of motion for a fractional order system ate studied. The fractional Hamilton principle in terms of Riesz fractional derivatives is established, and the fractional Lagrange equations and the fractional Hamilton canonical equations are derived from the fractional Hamilton principle. In the end, an example is given to illustrate the application of the results. [ABSTRACT FROM AUTHOR]

Abstract: We show that the orthogonality of order bounded finite rank operators to the identity operator on is equivalent to the continuity of the space . We also describe discrete elements in the space of order bounded linear maps transforming a Riesz space into a Dedekind complete Riesz space . Our description is the same as in Wickstead (1981)  but we obtain it making less restrictive, more natural assumptions and presenting a different proof. Additionally, we formulate a necessary and sufficient condition for the discreteness and continuity of . [Copyright &y& Elsevier]

Motivated by the need to have secure strong designate verifier signatures (SDVS) even in the presence of quantum computers, a post-quantum lattice-based SDVS scheme is proposed based on the hardness of the short integer solution problem (SIS) and the learning with errors problem (LWE). The proposed SDVS scheme utilizes the Bonsai trees and pre-image sample-able function primitives to generate the designate verifier signature (DVS). In this construction, the un- forge-ability is based on the hardness of the SIS problem which is proven in the random oracle model and the non-transferability is based on the hardness of the LWE problem. As an application of the proposed SDVS scheme, we design a strong designate verifier ring signature scheme (SDVRS) which satisfies non-transferability. It is proven that the identity of the signer is unconditionally protected not only for any third-party but also for the designate verifier. Under the hardness of the SIS problem, the proposed SDVRS scheme is proven to be existentially un-forgeable in the random oracle model. [ABSTRACT FROM AUTHOR]

In this paper we study some important structural properties of weak orthomorphisms. Some new results of such operators are presented. [ABSTRACT FROM AUTHOR]

We construct polynomial wavelets with compact support based on differentiating the proposed one-parametric basic finite polynomial wavelet of class Cm (0,1,…).. We show that derivatives of this basic wavelet of the order k, 1 ≤ k < 2 (m+1) in many cases are also wavelets, and the derivatives of the order 2(m+1) are nonreduced Haar functions. Some of the constructed wavelets are orthogonal bases, and in case of nonorthogonality they are Riesz bases. [ABSTRACT FROM AUTHOR]

Abstract: Let and be Banach lattices. Let be a vector sublattice of and be an order continuous positive compact (resp. weakly compact) operator. We show that if is an ideal or an order dense sublattice of , then has a norm preserving compact (resp. weakly compact) positive extension to which is likewise order continuous on . In particular, we prove that every compact positive orthomorphism on an order dense sublattice of extends uniquely to a compact positive orthomorphism on . [Copyright &y& Elsevier]

Abstract: In this paper, we study order convergence and the order convergence structure in the context of -distributive lattices. Particular emphasis is placed on spaces with additional algebraic structure: we show that on a Riesz algebra with -order continuous multiplication, the order convergence structure is an algebra convergence structure, and construct the convergence vector space completion of an Archimedean Riesz space with respect to the order convergence structure. [Copyright &y& Elsevier]

In this article, we present a survey of some new results obtained in [2,8] . First, we give a geometric Paley–Wiener theorem for the Dunkl transform in the crystallographic case. Next we describe more precisely the support of the distribution associated to Dunkl translations in higher dimension. We also investigate the L p → L q boundedness properties of the Riesz potentials I α κ and the related fractional maximal function M κ , α associated to the Dunkl transform. Finally we prove the L p -boundedness, (1 < p < ∞) of the Riesz transforms in the Dunkl setting. [ABSTRACT FROM AUTHOR]

The non-self adjoint Sturm-Liouville operators with periodic and anti-periodic boundary conditions are studied. The basis property in the space Lp(0,1) (p > 1) of the root functions of these operators is proved. For the basisness in Lp(0,1) the inequality in the F. Riesz's theorem is used. [ABSTRACT FROM AUTHOR]

One version of Mcshane integral with respect to a basis for the function with value in Dedekind complete Riesz space is introduced. The important properties are proved and also an application of the type of sandwich theorems is given. [ABSTRACT FROM AUTHOR]

The non-self adjoint Sturm-Liouville operators with periodic and anti-periodic boundary conditions are studied. The basis property in the space Lp(0; 1) (p > 1 ) of the root functions of these operators is proved. For the basisness in Lp(0; 1) the inequality in the F. Riesz's theorem is used. [ABSTRACT FROM AUTHOR]

In this paper, a general theorem concerning φ-∣T∣k factors of infinite series has been proved. [ABSTRACT FROM AUTHOR]

This paper studies the reconstruction of a function f belonging to a shift-invariant space from the set of its non-uniformly distributed local sampled values. Here it is shown that if the set of sampling X = {xj}j∈J satisfies a necessary density conditions, then we can recover the function f from the set of its samples geometrically fast using an iterative algorithm. In addition, the algorithm is analyzed when the data is perturbed by noise, and it is proved that a small perturbation on the set of samples causes only a small change of the original function. Moreover, it is given an upper estimate of the rate of convergence of the algorithm. On the other hand, if we assume that X is a separated set, then it is shown that X is a set of sampling and explicit stability bounds are given. [ABSTRACT FROM AUTHOR]

In this paper we outline a new theory about integral and differential calculus for Riesz space-valued mappings defined on suitable Riesz spaces. In our abstract context, we prove some theorems similar to the classical ones, like for example the Fundamental Formula of Calculus and the theorem about exchanging order between limits and derivatives. As applications, we give some results about power series, a fixed point theorem, and some models of differential functional equations. [ABSTRACT FROM AUTHOR]

Abstract: The paper is devoted to a question if the Levi property is preserved by direct sums and quotients. The three-space problem for the Levi and Lebesgue properties in topological Riesz spaces is also investigated. [Copyright &y& Elsevier]

Abstract: We show that a sequentially (τ)-complete topological vector lattice X τ is isomorphic to some L 1(μ), if and only if the positive cone can be written as X + = ℝ+ B for some convex, (τ)-bounded, and (τ)-closed set B ⊂ X + \ {0}. The same result holds under weaker hypotheses, namely the Riesz decomposition property for X (not assumed to be a vector lattice) and the monotonic σ-completeness (monotonic Cauchy sequences converge). The isometric part of the main result implies the well-known representation theorem of Kakutani for (AL)-spaces. As an application we show that on a normed space Y of infinite dimension, the “ball-generated” ordering induced by the cone Y + = ℝ+ (for ‖u‖ >) cannot have the Riesz decomposition property. A second application deals with a pointwise ordering on a space of multivariate polynomials. [Copyright &y& Elsevier]

Abstract: We prove that an x 0-quasinilpotent semigroup S of continuous positive linear operators on a locally convex solid Riesz space X has a common invariant subspace. Using this, a result which implies the main theorem of Abramovich, Aliprantis and Burkinshaw [J. Funct. Anal. 115 (1993) 418424] is also given. [Copyright &y& Elsevier]

Abstract: Finitely generated linearly ordered Riesz spaces are described, leading to a proof that the variety of Riesz spaces is generated as a quasivariety by the Riesz space ℝ of real numbers. The finitely generated Riesz spaces are also described: they are the subalgebras of real-valued function spaces on root systems of finite height. [Copyright &y& Elsevier]

Some kinds of integral, like variational, Kurzweil-Henstock and (SL)-integral are introduced and investigated in the context of Riesz-space-valued functions and with respect to abstract derivation bases. Some versions of the Fundamental Theorem of Integral Calculus are given. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we show mainly two results about uniformly closed Riesz subspaces of ℝ X containing the constant functions. First, for such a Riesz subspace E, we solve the problem of determining the properties that a real continuous functiondefined on a proper open interval of ℝshould have in order that the conditions “E is closed under composition with ” and “E is closed under inversion in X” become equivalent. The second result, reformulated in the more general frame of the Archimedean Riesz spaces with weak order unit e, establishes that E (e-uniformly complete and e-semisimple) is closed under inversion in C(Spec E) if and only if E is 2-universally e-complete. [Copyright &y& Elsevier]

Some kinds of integral, like variational, Kurzweil-Henstock and (SL)-integral are introduced and investigated in the context of Riesz-space-valued functions and with respect to abstract derivation bases. Some versions of the Fundamental Theorem of Integral Calculus are given. [ABSTRACT FROM AUTHOR]

In this paper we formulate a version of the Kondurar theorem and a generalization of the Itô formula for functions taking values in Riesz spaces with respect to a convergence, satisfying suitable axioms. When the involved space is the space of measurable functions, both convergence almost everywhere and convergence in probability are included. Finally we present some comments and possible applications of the Itô formula. [ABSTRACT FROM AUTHOR]

We study the stabilization problem of linear parabolic boundary control systems. While the control system is described by a pair of standard linear differential operators (L, τ), the corresponding semigroup generator generally admits no Riesz basis of eigenvectors. Very little information on the fractional powers of this generator is needed. In this sense our approach has enough generality as a prototype to be used for other types of parabolic systems. We propose in this paper a unified algebraic approach to the stabilization of a variety of parabolic boundary control systems. In the special case where the semigroup generator admits a Riesz basis, we also propose a new and simpler algebraic approach to the stabilization which is based on the so-called identity compensator. To show the usefulness of our approach, a class of linear boundary control systems of second order in t is introduced, to discuss the stabilization or the enhancement of stability of these systems. [ABSTRACT FROM AUTHOR]

Abstract: It has been recognised that order is closely linked with probability theory, with lattice theoretic approaches being used to study Markov processes but, to our knowledge, the complete theory of (sub, super) martingales and their stopping times has not been formulated on Riesz spaces. We generalize the concepts of stochastic processes, (sub, super) martingales and stopping times to Riesz spaces. In this paper we consider discrete time processes with bounded stopping times. [Copyright &y& Elsevier]

As a generalization of the notion of Riesz seminorm, a class of seminorms on directed partially ordered vector spaces is introduced, such that (1) every seminorm in the class can be extended to a Riesz seminorm on every larger Riesz space that is majorized and (2) a seminorm on an order dense linear subspace of a Riesz space is in the class if and only if it can be extended to a Riesz seminorm on the Riesz space. The latter property yields that if a directed partially ordered vector space has an appropriate Riesz completion, then a seminorm on the space is in the class if and only if it is the restriction of a Riesz seminorm on the Riesz completion. An explicit formula for the extension is given. The class of seminorms is described by means of a notion of solid unit ball in partially ordered vector spaces. Some more properties concerning restriction and extension are studied, including extension to L- and M-seminorms. [Copyright &y& Elsevier]

We study the behavior of Riesz multimorphisms on Archimedean f-algebras with unit element and focus on their different multiplicative aspects. [Copyright &y& Elsevier]

A correction to the research paper "Orthogonally Additive Polynomials On Dedekind σ-Complete Vector Lattices that was published in 2015 is presented.