Bǎrbosu and Muraru (2015) introduced the bivariate generalization of the q -Bernstein–Schurer–Stancu operators and constructed a GBS operator of q -Bernstein–Schurer–Stancu type. The concern of this paper is to obtain the rate of convergence in terms of the partial and complete modulus of continuity and the degree of approximation by means of Lipschitz-type class for the bivariate operators. In...

In this paper we investigate the lower Lipschitz continuity of minimal points of an arbitrary set A depending upon a parameter u . Our results are formulated with the help of the modulus of minimality. The crucial requirement which allows us to derive sufficient conditions for lower Lipschitz continuity of minimal points is that the modulus of minimality is at least linear. The obtained results...

In this paper we propose a numerical scheme for a class of backward stochastic differential equations (BSDEs) with possible path-dependent terminal values. We prove that our scheme converges in the strong L2 sense and derive its rate of convergence. As an intermediate step we prove an L2-type regularity of the solution to such BSDEs. Such a notion of regularity, which can be thought of as the m...

We construct polynomial approximations of Dzjadyk type (in terms of the k -th modulus of continuity, k ≥ 1 ) for analytic functions defined on a continuum E in the complex plane, which simultaneously interpolate at given points of E . Furthermore, the error in this approximation is decaying as e−cn α strictly inside E , where c and α are positive constants independent of the degree n of the app...

In [1] we introduced a new sequence of linear positive operators Mn to approximate unbounded continuous functions of exponential growth on [0,∞). As this sequence is saturated with O(n−1), to accelerate the rate of convergence we applied the technique of linear combination introduced by May [3] and Rathore et al. [4] to these operators. The object of the present paper is to study the phenomena ...