using a generalized spherical mean operator, we obtain a generalization of titchmarsh&apos;s theorem for the dunkl transform for functions satisfying the (&apos;; p)-dunkl lipschitz condition in the space lp(rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.

in this paper‎, ‎using a generalized dunkl translation operator‎, ‎we obtain a generalization of titchmarsh&apos;s theorem for the dunkl transform for functions satisfying the$(psi,p)$-lipschitz dunkl condition in the space $mathrm{l}_{p,alpha}=mathrm{l}^{p}(mathbb{r},|x|^{2alpha+1}dx)$‎, ‎where $alpha>-frac{1}{2}$.

This article is devoted to study of the autoconvolution equations and generalized Mittag-Leffler functions. These types of equations are given in terms of the Laplace transform convolution of a function with itself. We state new classes of the autoconvolution equations of the first kind and show that the generalized Mittag-Leffler functions are solutions of these types of equations. In view of ...

In automated deduction, the final goal is to achieve a fully automatic proof system: given a logical specification of a problem, take a high-performance theorem prover, and let it do the work. Unfortunately, this does not work in practice, not only because theorem provers often lack finding the proof within reasonable time, but also because the specification is error-prone. For the latter, in t...

C. & H. Kirchner, ed. 15 International Conference on Automated Deduction (CADE-15), LNAI 1421, pp. 317–331, c ©Springer Verlag, 1998. Abstract. We present a theorem proving environment for the development of reliable and efficient group communication systems. Our approach makes methods of automated deduction applicable to the implementation of real-world systems by linking the Ensemble group co...

The correspondence between natural deduction proofs and λ-terms is presented and discussed. A variant of the reducibility method is presented, and a general theorem for establishing properties of typed (first-order) λ-terms is proved. As a corollary, we obtain a simple proof of the Church-Rosser property, and of the strong normalization property, for the typed λ-calculus associated with the sys...

The main purpose of this paper is to establish some new results onthe superstability and stability via a fixed point approach forthe Pexiderized exponential equation, i.e.,$$|f(x+y)-g(x)h(y)|leq psi(x,y),$$where $f$, $g$ and $h$ are three functions from an arbitrarycommutative semigroup $S$ to an arbitrary unitary complex Banachalgebra and also $psi: S^{2}rightarrow [0,infty)$ is afunction. Fur...

In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by Bota et al. [M-F. Bota, A. Petrusel, G.Petrusel and B. Samet, Coupled fixed point theorems forsingle-valued operators in b-metric spaces, Fixed Point TheoryAppl. (2015) 2015:231]. Also, we prove that Perov-type fix...