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Abstract: In this paper we prove a new version of Cowling–Price''s theorem for the Dunkl transform on . [Copyright &y& Elsevier]

Abstract: This paper extends the Hille–Phillips functional calculus and rational approximations results due to R. Hersh, T. Kato, P. Brenner, and V. Thomée to generators of bi-continuous semigroups. The method yields error estimates for rational time-discretization schemes for such semigroups, in particular for dual semigroups, Feller semigroups such as the Ornstein–Uhlenbeck semigroup, the heat semigroup, semigroups induced by nonlinear flows, implemented semigroups, and evolution semigroups. Furthermore, the results provide error estimates for a new class of inversion formulas for the Laplace transform. [Copyright &y& Elsevier]

Abstract: In this paper we study the hyponormality and subnormality of 2-variable weighted shifts using the Schur product techniques in matrices. As applications, we generalize the result in [R. Curto, J. Yoon, Jointly hyponormal pairs of subnormal operators need not be jointly subnormal, Trans. Amer. Math. Soc. 358 (2006) 5135–5159, Theorem 5.2] and give a non-trivial, large class satisfying the Curto–Muhly–Xia conjecture [R. Curto, P. Muhly, J. Xia, Hyponormal pairs of commuting operators, Oper. Theory Adv. Appl. 35 (1988) 1–22] for 2-variable weighted shifts. Further, we give a complete characterization of hyponormality and subnormality in the class of flat, contractive, 2-variable weighted shifts with the condition that the norm of the 0th horizontal 1-variable weighted shift of T is a given constant. [Copyright &y& Elsevier]

Abstract: In this paper we discuss log-convex solutions of the second order to the functional equation with initial condition given by We prove that if g satisfies an appropriate asymptotic condition, then (E) admits at most one solution f, which is eventually log-convex of the second order. Moreover, f can be defined explicitly in terms of g. If, in addition, g is eventually log-concave of the second order, then (E) has exactly one eventually log-convex of the second order solution. Our results complement similar ones established by R. Webster [R. Webster, Log-convex solutions to the functional equation : Γ-type functions, J. Math. Anal. Appl. 209 (1997) 605–623] and generalize results obtained by L. Lupaş [L. Lupaş, The C-function of E.W. Barnes, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 1 (1990) 5–11]. [Copyright &y& Elsevier]

Abstract: In this paper we will investigate the stability of the generalized (pexiderized) sine functional equation [Copyright &y& Elsevier]

Abstract: Let be an integer number. In this paper, we investigate the generalized Hyers–Ulam–Rassias stability in Banach spaces and also Banach modules over a Banach algebra and a -algebra, and the stability using the alternative fixed point of an n-dimensional cubic functional equation in Banach spaces: [Copyright &y& Elsevier]

Using the Jordan algebras methods, specially the properties of Peirce decomposition and the Frobenius transformation, we compute the coefficients of the zeta functional equation, in the case of Jordan algebras of type II. As particular cases of our result, we can cite the case of V=M(n,R) studied by Gelbart [Mem. Amer. Math. Soc. 108 (1971)] and Godement and Jacquet [Zeta functions of simple algebras, Lecture Notes in Math., vol. 260, Springer-Verlag, Berlin, 1972], and the case of V=Herm(3,Os) studied by Muro [Adv. Stud. Pure Math. 15 (1989) 429]. Let us also mention, that recently, Bopp and Rubenthaler have obtained a more general result on the zeta functional equation by using methods based on the algebraic properties of regular graded algebras which are in one-to-one correspondence with simple Jordan algebras [Local Zeta Functions Attached to the Minimal Spherical Series for a Class of Symmetric Spaces, IRMA, Strasbourg, 2003]. The method used in this paper is a direct application of specific properties of Jordan algebras of type II. [Copyright &y& Elsevier]

This paper deals with the global uniform exponential stability independent of delay of time-delay linear and time-invariant systems subject to point and distributed delays for the initial conditions being continuous real functions except possibly on a set of zero measure of bounded discontinuities. It is assumed that the delay-free system as well as an auxiliary one are globally uniformly exponentially stable and globally uniform exponential stability independent of delay, respectively. The auxiliary system is typically a part of the overall dynamics of the delayed system but not necessarily the isolated undelayed dynamics as usually assumed in the literature. Since there is a great freedom in setting such an auxiliary system, the obtained stability conditions are very useful in a wide class of practical applications. [Copyright &y& Elsevier]

In this paper we use the Fre´chet, Clarke, and Mordukhovich coderivatives to obtain variants of the Ekeland variational principle for a set-valued map F and establish optimality conditions for set-valued optimization problems. Our technique is based on scalarization with the help of a marginal function associated with F and estimates of subdifferentials of this function in terms of coderivatives of F. [Copyright &y& Elsevier]

In this paper, nonlinear two point boundary value problems with p-Laplacian operators subject to Dirichlet boundary condition and nonlinear boundary conditions are studied. We show the existence of three positive solutions by the five functionals fixed point theorem. [Copyright &y& Elsevier]