Annals of Communications in Mathematics

AbstractThe main purpose of this article is to introduce a modification of q-Dunkl generalization of Szasz-operators. We obtain approximation results via well known Korovkin’s type theorem. Moreover, we obtain the order of approximation, rate of convergence, functions belonging to the Lipschitz class and some direct theorems.

AbstractOur main purpose of this article is to study the approximation properties of Szasz-Mirakjan-Kantorovich operators by introducing the non negative parameter ´ 0 5 [α]p,q 5 [β]p,q. For this purpose we define the Stancu variant of Szasz-Mirakjan- ´ Kantorovich operators via (p, q)-variant of Dunkl generalization. First we study the Korovkin’s type approximation results in weighted spaces. Finally, we obtain the convergence of our new operators in by use of modulus of continuity in Lipschitz class and Petter’s Kfunctionals. The extra parameter p provides more flexibility and a generalized version in approximation rather than q.

AbstractThe concept of statistical summability C, 1)(H, 1) has recently been introduced by [8]. In this paper we establish some inequalities related to concept of statistical summability (C, 1)(H, 1).