A Kantorovich-Stancu Type Generalization of Szasz Operators including Brenke Type Polynomials

We introduce a Kantorovich-Stancu type modification of a generalization of Szasz operators defined by means of the Brenke type polynomials and obtain approximation properties of these operators. Also, we give a Voronovskaya type theorem for Kantorovich-Stancu type operators including Gould-Hopper polynomials.

Density in Spaces of Interpolation by Hankel Translates of a Basis Function

The function spacesYm (m∈ℤ+)arising in the theory of interpolation by Hankel translates of a basis function, as developed by the authors elsewhere, are defined through a seminorm which is expressed in terms of the Hankel transform of each function and involves a weightw. At least two special classes of weights allow to write these indirect seminorms in direct form, that is, in terms of the function itself rather than its Hankel transform. In this paper, we give fairly general conditions onwwhich ensure that the Zemanian spacesℬμandℋμ (μ>−1/2)are dense inYm (m∈ℤ+). These conditions are shown to be satisfied by the weights giving rise to direct seminorms of the so-called type II.

Stability for a Class of Differential Equations with Nonconstant Delay

Stability is investigated for the following differential equations with nonconstant delayx't=qtFxt-ptfxt-τt,wherep:[0,+∞)→[0,+∞),q:[0,+∞)→R,τ:[0,+∞)→[0,r], andFandf:R→Rwithxfx>0 for x≠0 and x≤a(ais a positive constant) are continuous functions. A criterion is given for the zero solution of this delay equation being uniformly stable and asymptotically stable.

Applications of Littlewood-Paley Theory forB˙σ-Morrey Spaces to the Boundedness of Integral Operators

The boundedness of the various operators onB˙σ-Morrey spaces is considered in the framework of the Littlewood-Paley decompositions. First, the Littlewood-Paley characterization ofB˙σ-Morrey-Campanato spaces is established. As an application, the boundedness of Riesz potential operators is revisted. Also, a characterization ofB˙σ-Lipschitz spaces is obtained: and, as an application, the boundedness of Riesz potential operators onB˙σ-Lipschitz spaces is discussed.

On the Aleksandrov-Rassias Problems on Linearn-Normed Spaces

This paper generalizes T. M. Rassias' results in 1993 ton-normed spaces. IfXandYare two realn-normed spaces andYisn-strictly convex, a surjective mappingf:X→Ypreserving unit distance in both directions and preserving any integer distance is ann-isometry.

Analysis of Robust Stability for a Class of Stochastic Systems via Output Feedback: The LMI Approach

This paper investigates the robust stability for a class of stochastic systems with both state and control inputs. The problem of the robust stability is solved via static output feedback, and we convert the problem to a constrained convex optimization problem involving linear matrix inequality (LMI). We show how the proposed linear matrix inequality framework can be used to select a quadratic Lyapunov function. The control laws can be produced by assuming the stability of the systems. We verify that all controllers can robustly stabilize the corresponding system. Further, the numerical simulation results verify the theoretical analysis results.

Bifurcation of Limit Cycles and Center Conditions for Two Families of Kukles-Like Systems with Nilpotent Singularities

We solve theoretically the center problem and the cyclicity of the Hopf bifurcation for two families of Kukles-like systems with their origins being nilpotent and monodromic isolated singular points.

Generalized Analytic Fourier-Feynman Transform of Functionals in a Banach AlgebraℱA1,A2a,b

We introduce the Fresnel type classℱA1,A2a,b. We also establish the existence of the generalized analytic Fourier-Feynman transform for functionals in the Banach algebraℱA1,A2a,b.

On Solutions of Fractional Order Boundary Value Problems with Integral Boundary Conditions in Banach Spaces

The object of this paper is to investigate the existence of a class of solutions for some boundary value problems of fractional order with integral boundary conditions. The considered problems are very interesting and important from an application point of view. They include two, three, multipoint, and nonlocal boundary value problems as special cases. We stress on single and multivalued problems for which the nonlinear term is assumed only to be Pettis integrable and depends on the fractional derivative of an unknown function. Some investigations on fractional Pettis integrability for functions and multifunctions are also presented. An example illustrating the main result is given.