Volume 21, Issue 1

Abstract. We present a weighted Montgomery identity for the fractional integral of a function f with respect to another function g and use it to obtain weighted Ostrowski type inequalities for fractional integrals involving functions whose first derivatives belong to L p spaces. These inequalities are generally sharp in case p>1$p>1$ and best possible in case p=1$p=1$. Applications for the Hadamard fractional integrals are given.

Abstract. In this paper, new and general classes of multi-variable Hermite–Tricomi functions are introduced and some properties of these functions are established. Further, generating relations for Laguerre–Hermite polynomials involving various forms of Hermite–Tricomi functions are derived.

Abstract. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. The main purpose of this paper is to prove a *-version of Posner's theorem mentioned above. Moreover, we describe the structure of an arbitrary additive mapping which is *-centralizing on a prime ring with involution.

Abstract. The effective sufficient conditions are established for the unique solvability of the general linear boundary value problems for impulsive systems with singularities. The singularity is understood in the sense that the matrix and vector functions of a continuous (as well as of a discrete) argument which correspond to this system may be nonsummable. Analogous results are obtained for similar impulsive systems with small parameters.

Abstract. We prove the exponential law for partial and local maps.

Abstract. It is shown that the class of all non-separable extensions of a nonzero σ$\sigma $-finite Borel measure in the topological vector space ℝℕ$\mathbb {R}^{\mathbb {N}}$, which are invariant under some everywhere dense continual subgroup of ℝℕ$\mathbb {R}^{\mathbb {N}}$ and which possess the uniqueness property, has maximal cardinality 22c$2^{2^{c}}$. Some related questions concerning the measurability properties of real-valued functions with respect to the class of non-separable measures are also discussed.

Abstract. In this paper, we prove that if f is a transcendental meromorphic function of finite order which has two Borel exceptional values a (∈ℂ$\in \mathbb {C}$) and b (∈ℂ∪{∞}$\in \mathbb {C}\cup \lbrace \infty \rbrace $), and if f(z+η)-f(z)$f(z+\eta )-f(z)$ and f(z)$f(z)$ share values d (d∈ℂ$d\in \mathbb {C}$ and d≠a$d\ne a$), b CM, f(z)$f(z)$ is not periodic of period η$\eta $ (∈ℂ$\in \mathbb {C}$), then b=∞$b=\infty $, d≠a2,0$d\ne \frac{a}{2},0$ and f(z)=a+cec1z$f(z)=a+ce^{c_1z}$, where c,c1$c,c_1$ are two nonzero constants.

Abstract. The class of functions of s variables Hα/s(s)$H_{\alpha /s}^{(s)}$ is defined. For the functions of this class, Sász's theorem for s -dimensional Fourier–Haar series is proved. When α=1$\alpha =1$, it is shown that the obtained theorem is best possible for general complete orthonormal systems.

Abstract. In the present paper we study the Stancu variant of the Beta-Szász operators. We establish a direct result in terms of the modulus of continuity and an asymptotic formula in simultaneous approximation for these operators.

Abstract. We analyze Sierpiński's example of a real-valued Lebesgue measurable function on ℝ$\mathbb {R}$ which is not bounded from above by any real-valued Borel function. In this context, some real-valued step-functions with analogous properties are discussed.

Abstract. In this paper, using the topological interpretation of the Baer invariant 𝒱M(G)$\mathcal {V}M(G)$ of a group G with respect to an arbitrary variety 𝒱$\mathcal {V}$, we extend a result of Burns and Ellis [Math. Z. 226 (1997), 405–428] on the second nilpotent multiplier of a free product of two groups to the c -nilpotent multipliers for all c≥1$c\ge 1$. In particular, we show that M(c)(G*H)≅M(c)(G)⊕M(c)(H)$M^{(c)}(G\ast H)\cong M^{(c)}(G)\oplus M^{(c)}(H)$ when G and H are finite groups with some conditions or when G and H are two perfect groups.

Abstract. The aim of this paper is to present some properties of firmly nonexpansive operators in Hilbert spaces. As a consequence of the principal result, a fixed point theorem about nonexpansive operators is obtained.

Abstract. In this paper, the boundedness of some sublinear operators is proved on homogeneous Herz–Morrey spaces with variable exponent.