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...

We give a new proof of the small excess regularity theorems for integer multiplicity recti able currents of arbitrary dimension and codimension minimizing an elliptic parametric variational integral. This proof does not use indirect blow-up arguments, it covers interior and boundary regularity, it applies to almost minimizing currents, and it gives an explicit and often optimal modulus of conti...

In this paper we first introduce the King type modification of q-Bernstein-Chlodowsky operators, then we examine the rate of convergence of these operators by means of modulus of continuity and with the help of the functions of Lipschitz class. We proved that the error estimation of this modification is better than that of classical q-Bernstein-Chlodowsky operators whenever 0 ≤ x ≤ bn 2[n]+1 . ...