Strict s-numbers of the Volterra operator
For Volterra operator $V\colon L^1(0,1) \to C[0,1]$ and summation operator $σ\colon \ell^1 \to c$, we obtain exact values of Approximation, Gelfand, Kolmogorov, Mityagin and Isomorphism numbers.
math.FA↗
arXiv subjects
Taqseer Khan
Publications and source records attributed to Taqseer Khan.
Approximation properties of the Stancu type Dunkl generalization of the Kantorovich-Szász-Mirakjan-operators via q-calculus
In this paper we construct Stancu type q-Kantrovich-Szász-Mirakjan operators generated by Dunkl generalization of the exponential function. We obtain some approximation results using the Korovkin approximation theorem and the weighted Korovkin-type theorem for these operators. We also study convergence properties by using the modulus of continuity and the rate of convergence of these operators for functions belonging to the Lipschitz class. Furthermore, we obtain the rate of convergence in terms of the classical, second order, and weighted modulus of continuity.
math.CA↗
On approximation by Stancu type q-Bernstein-Schurer-Kantorovich operators
In this paper we introduce the Stancu type generalization of the q-Bernstein-Schurer-Kantorovich operators and examine their approximation properties. We investigate the convergence of our operators with the help of the Korovkin's approximation theorem and examine the convergence of these operators in the Lipschitz class of functions. We also investigate the approximation process for these operators through the statistical Korovkin's approximation theorem. Also, we present some direct theorems for these operators. Finally we introduce the bivariate analogue of these operators and study some results for the bivariate case.
math.CA↗
On statistical approximation properties of on statistical approximation properties of (p,q)-bleimann-butzer-hahn operators
The aim of this paper is to introduce a generalization of the (p,q)-Bleimann-Butzer-Hahn operators based on (p,q)-integers and obtain Korovkin's type statistical approximation theorem for these operators. Also, we establish the rate of convergence of these operators using the modulus of continuity. Furthermore, we introduce (p,q)-Bleimann-Butzer-Hahn bivariate operators.
math.CA↗