Статьи журнала - Владикавказский математический журнал
Все статьи: 983
Existence theorem for a fractal Sturm-Liouville problem
Статья научная
In this article, using a new calculus defined on fractal subsets of the set of real numbers, a Sturm-Lioville type problem is discussed, namely the fractal Sturm-Liouville problem. The existence and uniqueness theorem has been proved for such equations. In this context, the historical development of the subject is discussed in the introduction. In Section 2, the basic concepts of Fα-calculus defined on fractal subsets of real numbers are given, i.e., Fα-continuity, Fα-derivative and fractal integral definitions are given and some theorems to be used in the article are given. In Section 3, the existence and uniqueness of the solutions for the fractal Sturm-Liouville problem are obtained by using the successive approximations method. Thus, the well-known existence and uniqueness problem for Sturm-Liouville equations in ordinary calculus is handled on the fractal calculus axis, and the existing results are generalized.
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Exponential stability for a swelling porous-heat system with thermodiffusion effects and delay
Статья научная
In the present work, we consider a one-dimensional swelling porous-heat system with single time-delay in a bounded domain under Dirichlet-Neumann boundary conditions subject to thermodiffusion effects and frictional damping to control the delay term. The coupling gives new contributions to the theory associated with asymptotic behaviors of swelling porous-heat. At first, we state and prove the well-posedness of the solution of the system by the semigroup approach using Lumer-Philips theorem under suitable assumption on the weight of the delay. Then, we show that the considered dissipation in which we depended on are strong enough to guarantee an exponential decay result by using the energy method that consists to construct an appropriate Lyapunov functional based on the multiplier technique, this result is obtained without the equal-speed requirement. Our result is new and an extension of many other works in this area.
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Extension of an almost f-algebra multiplication
Статья научная
It is proved that an almost f-algebra multiplication and a d-algebra multiplication defined on a majorizing vector sublattice of a Dedekind complete vector lattice can be extended to the whole vector lattice by using purely algebraic and order theoretical means.
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Functional calculus and Minkowski duality on vector lattices
Статья научная
The paper extends homogeneous functional calculus on vector lattices. It is shown that the function of elements of a relatively uniformly complete vector lattice can naturally be defined if the positively homogeneous function is defined on some conic set and is continuous on some closed convex subcone. An interplay between Minkowski duality and homogeneous functional calculus leads to the envelope representation of abstract convex elements generated by the linear hull of a finite collection in a uniformly complete vector lattice.
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Functions with uniform sublevel sets on cones
Статья научная
Extended real-valued functions on a real vector space with uniform sublevel sets are important in optimization theory. Weidner studied these functions in [1]. In the present paper, we study the class of these functions, which coincides with the class of Gerstewitz functionals, on cones. These cone are not necessarily embeddable in vector spaces. Almost any Weidner's results are not true on cones without extra conditions. We show that the mentioned conditions are necessary, by nontrivial examples. Specially for element k from the cone P, we define k-directional closed subsets of the cone and prove some properties of them. For a subset A of the cone P, we characterize domain of the φA,k (function with uniform sublevel set) and show that this function is k-transitive. One of the important conditions for satisfying the results, is that k has the symmetric element in the cone. Also, we prove that, under some conditions, the class of Gerstewitz functionals coincides with the class of k-translative functions on P.
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Generalization of Eberlein's and sine's ergodic theorems to lr-nets
Статья научная
The notion of LR-nets provides an appropriate setting for study of various ergodic theorems in Banach spaces. In the present paper, we prove Theorems 2.1, 3.1 which extend Eberlein's and Sine's ergodic theorems to LR-nets. Together with Theorem 1.1, these two theorems form the necessary background for further investigation of strongly convergent LR-nets. Theorem 2.1 is due to F. Rabiger, and was announced without a proof in [1].
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Generalization of the Ostrowski inequalities on time scales
Статья научная
The idea of time scales calculus’ theory was initiated and introduced by Hilger (1988) in his PhD thesis order to unify discret and continuous analysis and to expend the discrete and continous theories to cases ``in between''. Since then, mathematical research in this field has exceeded more than 1000 publications and a lot of applications in the fields of science, i.e., operations research, economics, physics, engineering, statistics, finance and biology. Ostrowski proved an inequality to estimate the absolute deviation of a differentiable function from its integral mean. This result was obtained by applying the Montgomery identity. In the present paper we derive a generalization of the Montgomery identity to the various time scale versions such as discrete case, continuous case and the case of quantum calculus, by obtaining this generalization of Montgomery identity we would prove our results about the generalization of the Ostrowski inequalities (without weighted case) to the several time scales such as discrete case, continuous case and the case of quantum calculus and recapture the several published results of different authors of various papers and thus unify corresponding discrete version and continuous version. Similarly we would also derive our results about the generalization of the Ostrowski inequalities (weighted case) to the different time scales such as discrete case and continuous case and recapture the different published results of several authors of various papers and thus unify corresponding discrete version and continuous version. Moreover, we would use our obtained results (without weighted case) to the case of quantum calculus.
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Статья научная
The so called grand spaces nowadays are one of the main objects in the theory of function spaces. Grand Lebesgue spaces were introduced by T. Iwaniec and C. Sbordone in the case of sets Ω with finite measure |Ω|
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H-операторы в идеальных пространствах со смешанной квазинормой E (\ Omega)
Статья научная
Цель настоящей работы - с единой точки зрения рассмотреть поведение нелинейных операторов типа суперпозиции, интегральных операторов Гаммерштейна и Урысона в общих квазинормированных идеальных пространствах. Некоторые из нижеприведенных результатов анонсированы нами ранее в статье [1].
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![H\"Older type inequalities for orthosymmetric bilinear operators](/file/thumb/14318219/holder-type-inequalities-for-orthosymmetric-bilinear-operators.png "H\\"Older type inequalities for orthosymmetric bilinear operators")
H\"Older type inequalities for orthosymmetric bilinear operators
Статья научная
An interplay between squares of vector lattice and homogeneous functional calculus is considered and H\"older type inequalities for orthosymmetric bilinear operators are obtained.
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Hankel determinant of third kind for certain subclass of multivalent analytic functions
Статья научная
The objective of this paper is to obtain an upper bound (not sharp) to the third order Hankel determinant for certain subclass of multivalent (p-valent) analytic functions, defined in the open unit disc E. Using the Toeplitz determinants, we may estimate the Hankel determinant of third kind for the normalized multivalent analytic functions belongng to this subclass. But, using the technique adopted by Zaprawa [1], i.e., grouping the suitable terms in order to apply Lemmas due to Hayami [2], Livingston [3] and Pommerenke [4], we observe that, the bound estimated by the method adopted by Zaprawa is more refined than using upon applying the Toeplitz determinants.
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Hardy type inequalities in classical and grand Lebesgue spaces lp), 0
Статья научная
In 2020 Rovshan A. Bandaliev et al. proved the boundedness of Hardy operator for monotone functions in grand Lebesgue spaces Lp)(0,1), 0
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Homogeneous functions of regular linear and bilinear operators
Статья научная
Using envelope representations explicit formulae for computing \widehat{\varphi}(T_1,...,T_N) for any finite sequence of regular linear or bilinear operators T_1,...,T_N on vector lattices are derived.
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Increasing unions of Stein spaces with singularities
Статья научная
We show that if X is a Stein space and, if Ω⊂X is exhaustable by a sequence Ω1⊂Ω2⊂…⊂Ωn⊂… of open Stein subsets of X, then Ω is Stein. This generalizes a well-known result of Behnke and Stein which is obtained for X=Cn and solves the union problem, one of the most classical questions in Complex Analytic Geometry. When X has dimension 2, we prove that the same result follows if we assume only that Ω⊂⊂X is a domain of holomorphy in a Stein normal space. It is known, however, that if X is an arbitrary complex space which is exhaustable by an increasing sequence of open Stein subsets X1⊂X2⊂⋯⊂Xn⊂…, it does not follow in general that X is holomorphically-convex or holomorphically-separate (even if X has no singularities). One can even obtain 2-dimensional complex manifolds on which all holomorphic functions are constant.
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Inequalities for the Schwarzian derivative for subclasses of convex functions in the unit disc
Статья научная
Nehari norm of the Schwarzian derivative of an analytic function is closely related to its univalence. The famous Nehari--Kraus theorem [3, 4] and Ahlfors--Weill theorem [1] are of fundamental importance in this direction. For a non-constant meromorphic function f on D the unite disc, the Schwarzian derivative S_f of f by is holomorphic at z_0\in D if and only if f is locally univalent at z_0. The aim of this paper is to give sharp estimates of the Nehari norm for the subclasses of convex functions in the unit disc.
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Infinitely fine partitions of measures spaces
Статья научная
In any measurable space one can find a hyperfinite infinitesimal partition, that is, a hyperfinite set of disjoint inner (in the sense of nonstandard analysis) measurable subsets such that every standard measurable set is representable as a union of sets of this collection. In this paper we characterize the various properties of measures in terms of infinitesimal partitions. In particular, we characterize the non-atomicness of the measures and give a short proof of the Sobchik-Hammer theorem.
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Infinitesimals in ordered vector spaces
Статья научная
An infinitesimal approach to ordered spaces is proposed. Archimedean property and Dedekind completeness in ordered spaces are discussed from a nonstandard point of view.
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Статья научная
In this paper we consider classical solutions of an initial boundary value problem for a system of semilinear parabolic equations with absorption and nonlinear nonlocal boundary conditions. Nonlinearities in equations and boundary conditions may not satisfy the Lipschitz condition. To prove the existence of a solution we regularize the original problem. Using the Schauder–Tikhonov fixed point theorem, the existence of a local solution of regularized problem is proved. It is shown that the limit of solutions of the regularized problem is a maximal solution of the original problem. Using the properties of a maximal solution, a comparison principle is proved. In this case, no additional assumptions are made when nonlinearities in absorption do not satisfy the Lipschitz condition. Conditions are found under which solutions are positive functions. The uniqueness of the solution is established. It is shown that the trivial solution (0, 0) may not be unique.
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