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.

AbstractIn this paper, we introduce the algebra of tricomplex numbers as in idempo- tent forms and tricomplex polynomials as a generalization of the field of bicomplex num- bers. We describe how to define elementary functions in such an algebra, polynomials, Taylor series for tricomplex holomorphic functions, algebra of eigenvalues corresponding to an eigenvector on tricomplex space, and using a specific result, we define tricomplex polynomial, which is a better generalization of bicomplex polynomial.

AbstractIn this paper, we obtain some results on infinite products in bi-complex space, and the exact order of simultaneous results with quantitative estimate for the bi- complex gamma functions and bi-complex Beta functions. Finally using the specific re- sults of complex gamma operator and complex beta operator we introduce the bi-complex gamma functions and bi-complex beta operators and obtain some results.