Keywords: Baskakov-Szász operators Modulus of continuity Asymptotic formula Simultaneous approximation Statistical convergence Bounded variation a b s t r a c t In the present paper, we introduce generalized Baskakov-Szász type operators and study some approximation properties of these operators e.g., rate of convergence in ordinary and simultaneous approximation, statistical convergence and th...

We study the convergence of two stochastic approximation algorithms with randomized directions: the simultaneous perturbation stochastic approximation algorithm and the random direction Kiefer–Wolfowitz algorithm. We establish deterministic necessary and sufficient conditions on the random directions and noise sequences for both algorithms, and these conditions demonstrate the effect of the “ra...

We study the convergence of two stochastic approximation algorithms with randomized directions: the simultaneous perturbation stochastic approximation algorithm and the random direction Kiefer–Wolfowitz algorithm. We establish deterministic necessary and sufficient conditions on the random directions and noise sequences for both algorithms, and these conditions demonstrate the effect of the “ra...

For proving linear independence of real numbers, Hermite [6] considered simultaneous approximation to these numbers by algebraic numbers. The point of view introduced by Siegel in 1929 [14] is dual (duality in the sense of convex bodies): he considers simultaneous approximation by means of independent linear forms. We define the height of a linear form L = a0X0 + · · · + amXm with complex coeff...