Introduction 1. THIS paper embodies mainly the proof of results announced previously (Hayman (5)). Let f(z) be a non-constant integral function and p u t

Keywords: q-Bernstein–Schurer–Stancu operators q-integers Modulus of smoothness Rate of convergence a b s t r a c t In the present paper, we introduce the Stancu type generalization of the Bernstein–Schurer operators based on q integers. First, we prove the basic convergence of S ða;bÞ n;p ð:; q; xÞ and then obtain the rate of convergence by these operators in terms of the modulus of continuity...

For a function algebra A we investigate relations between the following three topics: isomorphisms of singly generated A-modules, Morita equivalence bimodules, and ‘real harmonic functions’ with respect to A. We also consider certain groups which are naturally associated with a uniform algebra A. We illustrate the notions considered with several examples.

some estimates are proved for the generalized fourier-bessel transform in the space (l^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

We have introduced and investigated the notion of I-extremal disconnectedness on ideal topological spaces. First, we found that the notions of extremal disconnectedness and I-extremal disconnectedness are independent of each other. About the letter one, we observed that every open subset of an I-extremally disconnected space is also an I-extremally disconnected space. And also, in extremally di...

In the present paper we introduce a q -analogue of the bivariate Durrmeyer operators. A convergence theorem for these operators is established and the rate of convergence in terms of modulus of continuity is determined. Also, a Voronovskaja type theorem has been investigated for these operators. Mathematics subject classification (2010): 41A10, 41A36.

Purpose: The purpose of this paper is to introduce the mixed summation-integral-type Lupaş-Phillips-Bernstein operators. Methods: Firstly, we compute the moments of the operators. We use the method of Korovkin-type statistical approximation and modulus of continuity. Results: We find the rate of convergence of the modified operators using statistical convergence and modulus of continuity. Concl...

In this paper, we discuss properties of convergence for a modification of the q-Bernstein operators. Using the notion of A-statistical approximation, where A is a nonnegative regular summability matrix, we investigate the Korovkin type statistical approximation properties of this modification via A-statistical approximation. For 0 < q ≤ 1, we obtain that the q-Bernstein operators is A-statistic...