Inclusion Theorems Research Articles

M-positive semi-definiteness and M-positive definiteness of fourth-order partially symmetric Cauchy tensors

Inspired by symmetric Cauchy tensors, we define fourth-order partially symmetric Cauchy tensors with their generating vectors. In this article, we focus on the necessary and sufficient conditions for the M-positive semi-definiteness and M-positive definiteness of fourth-order Cauchy tensors. Moreover, the necessary and sufficient conditions of the strong ellipticity conditions for fourth-order Cauchy tensors are obtained. Furthermore, fourth-order Cauchy tensors are M-positive semi-definite if and only if the homogeneous polynomial for fourth-order Cauchy tensors is monotonically increasing. Several M-eigenvalue inclusion theorems and spectral properties of fourth-order Cauchy tensors are discussed. A power method is proposed to compute the smallest and the largest M-eigenvalues of fourth-order Cauchy tensors. The given numerical experiments show the effectiveness of the proposed method.

E-eigenvalue inclusion theorems for tensors

Two Z-eigenvalue inclusion theorems for tensors presented by Wang et al. (Discrete Cont. Dyn.-B, 2017, 22(1): 187-198) are first generalized to E-eigenvalue inclusion theorems. And then a tighter E-eigenvalue inclusion theorem for tensors is established. Based on the new set, a sharper upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.

λ-double statistical convergence of functions

In this paper, the definitions of ?-double strong summability and ?-double statistical convergence for real valued measurable functions of two variables defined on (1,?)x(1,?) are presented. Using these definitions we present a series of basic results. Additionally, inclusion theorems, extension of existing results in the literature, and their variations have been established.

Lacunary distributional convergence in topological spaces

Most of the summability methods cannot be defined in an arbitrary Hausdorff topological space unless one introduces a linear or a group structure. In the present paper, using distribution functions over the Borel ?-field of the topology and lacunary sequences we define a new type of convergencemethod in an arbitrary Hausdorff topological space and we study some inclusion theorems with respect to the resulting summability method. We also investigate the inclusion relation between lacunary sequence and lacunary refinement of it.

On I-Asymptotically Lacunary Statistical Equivalence of Functions on Amenable Semigroups

In this study we define the notions of asymptotically paper, we introduce the concept of Iasymptotically statistical equivalent and I-asymptotically lacunary statistical equivalent functions defined on discrete countable amenable semigroups. In addition to these definitions, we give some inclusion theorems.

Some new sequence spaces defined by bounded variation in 2-normed spaces

In this paper, by using Orlicz function and almost lacunary bounded variation we introduce and examine a new sequence space in 2-normed spaces. We also study some basic topological and algebraic properties of these spaces. In addition, we shall established inclusion theorems between these sequence spaces.

On the difference spaces of almost convergent and strongly almost convergent double sequences

In this paper, we study the difference spaces $${\mathcal {F}}(\varDelta )$$, $${\mathcal {F}}_0(\varDelta )$$, $${\mathcal {[F]}}(\varDelta )$$ and $${\mathcal {[F]}}_0(\varDelta )$$ of double sequences obtained as the domain of four-dimensional backward difference matrix $$\varDelta $$ in the spaces $${\mathcal {F}}$$, $${\mathcal {F}}_{0}$$, $${\mathcal {[F]}}$$ and $${\mathcal {[F]}}_{0}$$ of almost convergent, almost null, strongly almost convergent and strongly almost null double sequences; respectively. We examine general topological properties of those spaces and give some inclusion theorems. Furthermore, we deal with their dual spaces.

C-eigenvalue inclusion theorems for piezoelectric-type tensors

C-eigenvalues and C-eigenvectors of piezoelectric-type tensors play an important role in piezoelectric effect and converse piezoelectric effect. In this article, with the help of components of C-eigenvectors, we present three inclusion theorems to locate all C-eigenvalues for a given piezoelectric-type tensor. Finally, numerical examples are reported to be tighter than the S-partition method presented by Li and Li (2017).

Pointwise estimates in the Filippov lemma and Filippov-Ważewski theorem for fourth order differential inclusions

In this work we give a generalization of the Filippov-Ważewski Theorem to the fourth order differential inclusions in a separable complex Banach space $\mathbb{X}$ \begin{equation*} \mathcal{D}y=y^{\prime \prime \prime \prime }-( A^{2}+B^{2}) y^{\prime \prime }+A^{2}B^{2}y\in F( t,y) , \end{equation*} with the initial conditions in $c\in \lbrack 0,T]$ \begin{equation} y( c) =\alpha ,\qquad y^{\prime }( c) =\beta ,\qquad y^{\prime \prime }( c) =\gamma ,\qquad y^{\prime \prime \prime }( c) =\delta , \label{*} \end{equation} We assume that the multifunction $F:\left[ 0,T\right] \times \mathbb{X}% \leadsto c( \mathbb{X}) $ is Lipschitz continuous in $y$ with the integrable Lipschitz constant $l( .) $, while $A^{2},B^{2}\in B( \mathbb{X}) $ are the infinitesimal generators of two cosine families of operators. The main result is the following version of Filippov Lemma: \medskip {\sc Theorem:} {\it Let $y_{0}\in W^{4,1}=W^{4,1}([ 0,T] ,\mathbb{X}) $ be such function with \rom{(\ref{*})} that \begin{equation*} \mathrm{dist}( \mathcal{D}y_{0}( t) ,F( t,y_{0}( t) ) ) \leq p_{0}( t) \quad \text{a.e.\ in } [ c,d] \subset [ 0,T] , \end{equation*}% where $p_{0}\in L^{1}[ 0,T] $. Then there are $\mathcal{\sigma }_{0}$ \rom{(}depending on $p_{0})$ and $\varphi $ such that for each $\varepsilon > 0$\ there exists a solution $y\in W^{4,1}$ of the above problem such that almost everywhere in $t\in \lbrack c,d]$ we have $\vert \mathcal{D}y( t) -\mathcal{D}y_{0}( t) \vert \leq \mathcal{\sigma }_{0}( t) $, \begin{alignat*}2 \vert y( t) -y_{0}( t) \vert &\leq(\varphi \ast _{c}\sigma _{0})( t) , &\qquad \vert y^{\prime }( t) -y_{0}^{\prime }( t) \vert \leq ( \varphi ^{\prime }\ast _{c}\sigma _{0}t) ( t ) , \\ \vert y^{\prime \prime }( t) -y_{0}^{\prime \prime }( t) \vert &\leq ( \varphi ^{\prime \prime }\ast _{c}\sigma _{0}) ( t) &\qquad \vert y^{\prime \prime \prime }( t) -y_{0}^{\prime \prime \prime }( t) \vert \leq( \varphi ^{\prime \prime \prime }\ast _{c}\sigma _{0})( t) , \end{alignat*}% where $\ast _{c}$ stands for the convolution started at $c$.} Our estimates are constructive and more precise then those in the known versions of Filippov Lemma.

Inclusion theorems associated with a certain new family of asymptotically and statistically equivalent functions

Inclusion theorems associated with a certain new family of asymptotically and statistically equivalent functions

On the two-state problem for general differential operators

In this note we generalize the Ball-James rigidity theorem for gradient differential inclusions to the setting of a general linear differential constraint. In particular, we prove the rigidity for approximate solutions to the two-state inclusion with incompatible states for merely L1-bounded sequences. In this way, our theorem can be seen as a result of compensated compactness in the linear-growth setting.

An Implicit Function Theorem for Inclusions Defined by Close Mappings

The paper deals with the question of the solvability of inclusions F(x, σ) ∈ Q for mappings F close, in some metrics, to a given mapping F.

Variants of the Inequalities of Paley and Zygmund

We examine versions of the classical inequalities of Paley and Zygmund for functions of several variables. A sharp multiplier inclusion theorem and variants on the real line are obtained.

Riesz almost lacunary multiple triple sequence spaces of $\Gamma^{3}$ defined by a Musielak-Orlicz function

In this paper we introduce a new concept for Riesz almost lacunary $\Gamma^{3}$ sequence spaces strong $P-$ convergent to zero with respect to an Musielak-Orlicz function and examine some properties of the resulting sequence spaces. We also introduce and study statistical convergence of Riesz almost lacunary $\Gamma^{3}$ sequence spaces and also some inclusion theorems are discussed.

An Implicit Function Theorem for Inclusions Defined by Close Mappings

Рассматривается вопрос об условиях разрешимости включений $F(x,\sigma)\in Q$ для отображений $F$, близких, в тех или иных метриках, к некоторому заданному отображению $\widehat{F}$. Библиография: 4 названия.

Subclass of uniformly convex functions defined by linear operator

Making use of certain linear operator, we define a new subclass of uniformly convex functions with negative coefficients and obtain coefficient estimates, extreme points, closure and inclusion theorems and the radii of star likeness and convexity for the new subclass. Furthermore, results partial sums are discussed.

The backward operator of double almost $\left(\lambda_{m}\mu_{n}\right)$ convergence in $\chi^{2}-$Riesz space defined by a Musielak-Orlicz function

In this paper we introduce the backward operator is $\nabla$ and study the notion of $\nabla-$ statistical convergence and $\nabla-$ statistical Cauchy sequence using by almost $\left(\lambda_{m}\mu_{n}\right)$ convergence in $\chi^{2}-$Riesz space and also some inclusion theorems are discussed.

A regularity principle in sequence spaces and applications

We prove a nonlinear regularity principle in sequence spaces which produces universal estimates for special series defined therein. Some consequences are obtained and, in particular, we establish new inclusion theorems for multiple summing operators. Of independent interest, we settle all Grothendieck's type (ℓ1,ℓ2) theorems for multiple summing multilinear operators. We further employ the new regularity principle to solve the classification problem concerning all pairs of admissible exponents in the anisotropic Hardy–Littlewood inequalities.

Multiple summing maps: Coordinatewise summability, inclusion theorems and p-Sidon sets

We discuss the multiple summability of a multilinear map T:X1×⋯×Xm→Y when we have information on the summability of the maps it induces on each coordinate. Our methods have applications to inclusion theorems for multiple summing multilinear mappings and to the product of p-Sidon sets.

Smooth Lyapunov Functions for Multistable Differential Inclusions

We provide a converse Lyapunov theorem for differential inclusions with upper semicontinuous right-hand side, admitting a finite number of compact, globally attractive, weakly invariant sets, and evolving on Riemannian manifolds. Such properties entail multistable behavior in differential inclusions and may gather interest in a number of applications where uncertainty and discontinuities of the vector field play a major role.