Volume 20, Issue 4

Abstract. In this paper we obtain a Jensen's type inequality for operator-valued integrable functions, which generalizes some of the previous results in this regard. More precisely, if is a probability measure space and if ν is an operator convex function, then, under suitable conditions, we show that , where is assumed to be Bochner integrable and is a measurable function with .

Abstract. Let K be a commutative ring with unity, R be a non-commutative prime K -algebra of characteristic different from 2, U be the Utumi quotient ring of R , C be the extended centroid of R , and G and H be two non-zero generalized derivations of R . Suppose that is a non-central multilinear polynomial over K and there exists such that for all . Then one of the following holds: (1) there exist such that and for all , with ; (2) is central-valued on R and there exist such that and for all , with .

Abstract. The notion of (ψ,γ)-stability of the Jensen functional equation was introduced in [Nonlinear Funct. Anal. Appl. 11 (2006), 759–791] and it was shown that the Jensen functional equation is (ψ,γ)-stable on any step-two nilpotent group. In this paper, we prove a more general result by showing that the Jensen functional equation is (ψ,γ)-stable on step-three nilpotent groups.

Abstract. In this paper, we characterize the analytic self-maps ϕ of the unit disk 𝔻 in ℂ that induce continuous and compact composition operators from the logarithmic Bloch spaces, introduced by Stević [Appl. Math. Comput. 215 (2009), 841–849], into the μ-Bloch space, where μ is any weight defined on 𝔻. We give characterizations in terms of quotients of the logarithmic Bloch norm of the n -th power of ϕ and the μ-Bloch norm of the n -th power of the identity function I on 𝔻. This solves partially the problem proposed by Zhao [Proc. Amer. Math. Soc. 138 (2010), 2537–2546].

Abstract. The present paper deals with a new polynomial set and the application of the -transform on it.

Abstract. The optimal sufficient conditions for local solvability of the Cauchy problem for singular in phase variables nonlinear ordinary differential equations of higher orders are established.

Abstract. We prove the necessary and sufficient condition governing the weighted boundedness of the majorants for Fourier integrals Cesáro summation means in variable exponent Lebesgue spaces. Based on this result a weighted version of the well-known Bernstein inequality on the derivative of exponential type entire functions of finite order is established.

Abstract. In this paper, we give two characterization theorems to introduce new examples of basic hypergeometric d -orthogonal polynomials which, on the one hand, generalize the known q -Meixner, big q -Laguerre, little q -Laguerre and q -Laguerre polynomials and, on the other hand, can be viewed as q -analogs of d -orthogonal polynomials of Meixner and Laguerre type. For the resulting polynomials, we state some properties.

Abstract. Let Γ be a simple rectifiable closed Carleson curve and be its measurable bounded nonzero function on Γ. It is proved in the paper that the factorization of such a function in the class of Cauchy type integrals with density from the Lebesgue space L p (·) (Γ;ω) with variable exponent is equivalent to the property of the singular integral operator , where is the operator generated by a Cauchy singular operator, to be Noetherian in the space L p (·) (Γ;ω). This result generalizes a theorem of I. B. Simonenko.

Abstract. We introduce a new concept “GA-ɛ-convex function” and establish some integral inequalities of Simpson type for GA-ɛ-convex functions.

Abstract. In this paper we obtain fixed and common fixed point theorems for self-mappings defined on a closed and convex subset C of a quasi-Banach space. We give also a constructive method for finding the common fixed points of the involved mappings. As an application we obtain a result of the existence of solutions of integral equations.

Abstract. If are orthogonal matrices, in this paper we obtain strong and weak estimates for certain integral operators with kernels of the form , in the context of Lebesgue spaces with variable exponents.

Abstract. The 𝒦( J )-density topology defined in [Real Anal. Exchange 32 (2006/07), 273–286] is not regular. Making some modification in the definition of a 𝒦( J )-density point, we obtain the deep 𝒦( J )-density topology, which is completely regular. In this paper this topology is described and some of its properties are examined.