Volume 26, Issue 1

In this paper, we consider a one-dimensional porous thermoelastic system with second sound and nonlinear feedback. We show the well-posedness, using the semigroup theory, and establish an explicit and general decay rate result, using some properties of convex functions and the multiplier method. Our result is obtained without imposing any restrictive growth assumption on the damping term.

In this paper, we consider the weighted spaces of holomorphic functions on some open subsets of the complex plane and characterize the isomorphism classes of these spaces whenever our weights are warped and satisfy certain growth conditions.

We are concerned with the ν-th order nabla fractional q -difference equation (quantum equation) ∇q,ρ⁢(1)ν⁡x⁢(t)=c⁢(t)⁢x⁢(t),t∈qℕ1\nabla^{\nu}_{{q,\rho(1)}}x(t)=c(t)x(t),t\in q^{\mathbb{N}_{1}}, where q>1{q>1}, ℕ1={1,2,…}{\mathbb{N}_{1}=\{1,2,\dots\}}, ρ⁢(1)=q-1{\rho(1)=q^{-1}}. We prove that for 0<ν<1{0<\nu<1} and c⁢(t)≤0{c(t)\leq 0}, t∈ℕ1{t\in\mathbb{N}_{1}}, any solution of the q -difference equation with x⁢(1)>0{x(1)>0} satisfies limt→∞⁡x⁢(t)=0\lim_{t\to\infty}x(t)=0. This asymptotic result shows that the solutions of the nabla fractional q -difference equation ∇q,ρ⁢(1)ν⁡x⁢(t)=c⁢x⁢(t){{\nabla^{\nu}_{{q,\rho(1)}}}x(t)=cx(t)}, 0<ν<1{0<\nu<1}, c<0{c<0}, have asymptotic behavior similar to that of the solutions of the first order nabla q -difference equation ∇q⁡x⁢(t)=c⁢x⁢(t){\nabla_{q}x(t)=cx(t)}, c<0{c<0}, t∈qℕ1{t\in q^{\mathbb{N}_{1}}}.

We prove that, under certain restrictions, every locally compact group equipped with a nonzero, σ-finite, regular left Haar measure can be decomposed into two small sets, one of which is small in the sense of measure and the other is small in the sense of category, and all such decompositions originate from a generalised notion of a Lebesgue point. Incidentally, such class of topological groups for which this happens turns out to be metrisable. We also observe an interesting connection between Luzin sets in such spaces and decompositions of the above type.

The aim of this paper is to investigate the problem of control by the initial conditions of the heat equation with an integral boundary condition. Using the truncation method with an a posteriori parameter choice rule, we give the error estimate between the exact and the regularized solutions. A numerical implementation shows the efficiency of the proposed method.

In this article, we investigate the uniqueness problem on a transcendental entire function f⁢(z){f(z)} with its linear mixed-operators Tf , where T is a linear combination of differential-difference operators Dην:=f(ν)⁢(z+η){D^{\nu}_{\eta}:=f^{(\nu)}(z+\eta)} and shift operators Eζ:=f⁢(z+ζ){E_{\zeta}:=f(z+\zeta\/)}, where η,ν,ζ{\eta,\nu,\zeta} are constants. We obtain that if a transcendental entire function f⁢(z){f(z)} satisfies λ⁢(f-α)<σ⁢(f)<+∞{\lambda(f-\alpha)<\sigma(f\/)<+\infty}, where α⁢(z){\alpha(z)} is an entire function with σ⁢(α)<1{\sigma(\alpha)<1}, and if f and Tf share one small entire function a⁢(z){a(z)} with σ⁢(a)<σ⁢(f){\sigma(a)<\sigma(f\/)}, then T⁢f-a⁢(z)f⁢(z)-a⁢(z)=τ,{\frac{Tf-a(z)}{f(z)-a(z)}=\tau,} where τ is a non-zero constant. Furthermore, we obtain the value τ and the expression of f by imposing additional conditions.

The aim of this paper is to consider a generalized mixed variational-like inequality problem and prove a Minty-type lemma for its related auxiliary problems in a real Banach space. We prove the existence of a solution of these auxiliary problems. Further, we prove some properties of a solution set of generalized mixed variational-like inequality problems. Furthermore, we use a hybrid projection method to find a common element of a solution set of a system of unrelated generalized mixed variational-like inequality problems for generalized relaxed α-monotone mappings and the set of fixed points of a common fixed point problem for a family of generalized asymptotically quasi-ϕ-nonexpansive mappings in a reflexive, uniformly smooth and strictly convex Banach space.

It is shown that there exists a family of 22ℵ0{2^{2^{\aleph_{0}}}} non-isomorphic separable primary groups with unbounded basic subgroups of cardinality not exceeding 2ℵ0{2^{\aleph_{0}}}, where the cotorsion hull of each group is not fully transitive.

In this paper, we consider a Neumann problem for a linear elliptic equation with lower-order terms. A comparison result for solutions of the problem is proved by using Steiner symmetrization.

In the papers [1] and [6], for an inverse sequence of pointed topological spaces and fibrations preserving the base points E=E1←p1E2←p2⋯←pmEm+1,E=E_{1}\xleftarrow{p_{1}}E_{2}\xleftarrow{p_{2}}\cdots\xleftarrow{p_{m}}E_{m+1}, there exists an exact sequence *→lim←(1)[X,ΩEm]→[X,lim←E]→lim←(1)[X,Em]→*.*\rightarrow{\varprojlim}^{(1)}[X,\Omega E_{m}]\rightarrow[X,\varprojlim E]% \rightarrow{\varprojlim}^{(1)}[X,E_{m}]\rightarrow*. In the present paper, for an inverse sequence of pointed topological semi-simplicial sets and fibrations preserving base points E¯=E¯←p11E¯←p22⋯←pmE¯←m+1⋯,\underline{E}=\underline{E}{}_{1}\xleftarrow{p_{1}}\underline{E}{}_{2}% \xleftarrow{p_{2}}\cdots\xleftarrow{p_{m}}\underline{E}{}_{m+1}\xleftarrow{% \hphantom{p_{1}}}\cdots, an analogous formula is proved.

In this paper, we obtain the boundedness of the Marcinkiewicz integral on continual Herz spaces with variable exponent, where all parameters defining the space are variable.

In the present paper the sufficient conditions are obtained for the generalized r -absolute convergence (0<r<2{0<r<2}) of the single Fourier trigonometric series in terms of the modulus of δ-variation of a function. It is proved that these conditions are unimprovable in a certain sense. The classical results of Berstein, Szasz, Zygmund and others, related to the absolute convergence of single trigonometric Fourier series, were previously generalized by [L. Gogoladze and R. Meskhia, On the absolute convergence of trigonometric Fourier series, Proc. A. Razmadze Math. Inst. 141 2006, 29–40].

In this paper we introduce a new function space Bp,θ,a,ϰ,τ〈l〉⁢(s,G){B_{p,\theta,a,\varkappa,\tau}^{\langle l\rangle}(s,G)} with parameters of many groups of variables of Besov–Morrey type. In view of the embedding theorems we study some properties of the functions which belong to these spaces.

In this paper we investigate a new (α,β){(\alpha,\beta)}-metric F=β+a⁢α2+β2α{F=\beta+\frac{a\alpha^{2}+\beta^{2}}{\alpha}}, where α=ai⁢j⁢yi⁢yj{\alpha=\sqrt{{a_{ij}y^{i}y^{j}}}} is a Riemannian metric; β=bi⁢yi{\beta=b_{i}y^{i}} is a 1-form and a∈(14,+∞){a\in(\frac{1}{4},+\infty)} is a real scalar. Also, we investigate the relationship between the geodesic coefficients of the metric F and the corresponding geodesic coefficients of the metric α.

In this paper, we establish the spread relation of E -valued meromorphic functions and give some of its applications.

In this paper, we introduce the new notions of Lp{L_{p}}-intersection and mixed intersection bodies. Inequalities for the q -dual volume sum of Lp{L_{p}}-mixed intersection bodies are established.