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 ...

In this paper, a new analogue of Bernstein-Kantorovich operators as (p, q)-Bernstein-Kantorovich operators are introduced. We discuss approximation properties for these operators based on Korovkin’s type approximation theorem and we compute the order of convergence using usual modulus of continuity and also the rate of convergence when the function f belongs to the class LipM (α). Moreover, the...

In the present paper we introduce the GBS (Generalized Boolean Sum) operators of Durrmeyer type based on q -integers and the approximation of B-continuous functions using the above operators is studied. In addition, a uniform convergence theorem is established and the degree of approximation in terms of mixed modulus of continuity is evaluated. The study contains in the last section numerical c...

In this paper, we construct a form of linear positive operators with Brenke type polynomials as a generalization of Szasz-Durrmeyer operators. We obtain convergence properties of our operators with the help of the universal Korovkin-type property and calculate the order of approximation by using classical modulus of continuity. Explicit examples of our operators involving some orthonogal and d-...

In this paper, we present a sequence of linear positive bivariate operators and investigate the approximation properties of them. Next we study the rates of converge of this approximation by means modulus of continuity and functions from Lipschitz class. After we give a Voronovskaya type theorem for n Morever, we give an r th order generalization of these operators. Finally, we investigate appr...

In the present paper we introduce positive linear operators q−Bernstein Chlodowsky polynomials on a rectangular domain and obtain their Korovkin type approximation properties. The rate of convergence of this generalization is obtained by means of the modulus of continuity, and also by using the K-functional of Peetre. We obtain weighted approximation properties for these positive linear operato...

In this paper, we construct a linear positive operators q-parametric Szász Mirakjan operators generated by the q-Dunkl generalization of the exponential function. We obtain Korovkin’s type approximation theorem for these operators and compute convergence of these operators by using the modulus of continuity. Furthermore, the rate of convergence of the operators for functions belonging to the Li...