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In the present paper, we study the mixed summation integral type operators having Baskakov and Szász basis functions in summation and integration form, respectively. We also give here the alternate form of the operators in terms of hypergeometric functions and estimated moments of these operators using hypergeometric series. In the last section, we present some results for operators related to convergence. [ABSTRACT FROM AUTHOR]

In this paper, a kind of modified Baskakov–Schurer–Szász operators (1.2) is introduced. Approximation properties of theses operators are explored: the rate of convergence in terms of the usual moduli of smoothness is given, the convergence in certain weighted spaces is investigated. Furthermore, we study q -analogues of Baskakov–Schurer–Szász operators and its Stancu generalization. Then the better error estimations for the operators (6.3) by using King type approach is investigated. In the last section the Korovkin type weighted statistical approximation property of operators (9.1) is given. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study a simple integral generalization of q-analog of well known Bernstein operators with two parameters α and β, which was introduced in Mishra and Patel (2013) [17]. We give detail proof of the rate of convergence and Voronovskaja type asymptotic formula for the operators Dn, qα, β . Also, we establish statistical convergence for these operators and discuss modification of the operators Dn, qα, β for better approximation results over compact interval. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, a new theorem on the degree of approximation of function conjugate to a 2π periodic function f belonging to the generalized weighted Lipschitz -class by dropping the monotonicity condition on the generating sequence {pn } has been established which in turn generalizes the results of Lal (2009) [12] on Fourier series. We also note some errors appearing in the paper of Lal (2009) [12] and rectify them in the view of observations of Rhoades et al. (2011) [22]. [Copyright &y& Elsevier]