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Md. Nasiruzzaman

Publications and source records attributed to Md. Nasiruzzaman.

9 recordsLinked to original sources
arXiv2022

Approximation by q-Bernstein-Stancu-Kantorovich operators with shifted knots of real parameters

Our main purpose of this article is to study the convergence and other related properties of q-Bernstein-Kantorovich operators including the shifted knots of real positive numbers. We design the shifted knots of Bernstein-Kantorovich operators generated by the basic q-calculus. More precisely, we study the convergence properties of our new operators in the space of continuous functions and Lebesgue space. We obtain the degree of convergence with the help of modulus of continuity and integral modulus of continuity. Furthermore, we establish the quantitative estimates of Voronovskaja-type.

math.GM↗
arXiv2016

Modified Stancu-type Dunkl generalization of Szasz- Kantorovich-operators

In this paper, we introduce a modification of the Szasz-Mirakjan-Kantorovich operators as well as Stancu operators [9] (or a Dunkl generalization of modified Szasz-Mirakjan-Kantrovich operators [5]) which preserve the linear functions. These types of operators modification enables better error estimation than the classical Dunkl Szasz-MirakjanKantrovich as well as Stancu operators. We obtain some approximation results via well known Korovkin's type theorem, weighted Korovkin's type theorem convergence properties by using the modulus of continuity and the rate of convergence of the operators for functions belonging to the Lipschitz class

math.CA↗
arXiv2016

Approximation properties on q -Szasz-Mirakjan-Kantrovich Stancu type operators via Dunkl generalization

This paper is devoted to study the approximation properties and rate of approximation of the Szasz-Mirakjan-Kantrovich-Stancu type polynomials generated by the Dunkl generalization of the exponential function with respect to q -calculus. We present approximation properties with the help of well-known Korovkin's theorem and determine the rat e of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K-functional, and the second-order modulus of continuity. Moreover, we obtain the approximation results for Bivariate case for these operators

math.CA↗
arXiv2015

A Dunkl generalization of q-parametric Szasz-Mirakjan operators

In this paper, we construct a linear positive operators q-parametric Szasz-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 Lipschitz class is presented.

math.CA↗
arXiv2015

Some approximation properties of bivariate Bleimann-Butzer and Hahn operators based on (p,q)-integers

Recently, Mursaleen et al applied (p,q)-calculus in approximation theory and introduced (p,q)-analogue of Bernstein operators in [16]. In this paper, we construct and introduce a generalization of the bivariate Bleimann-Butzer-Hahn operators based on (p,q)-integers and obtain Korovkin type approximation theorem of these operators. Furthermore, we compute the rate of convergence of the operators by using the modulus of continuity and Lipschitz type maximalfunctions.

math.CA↗
arXiv2015

On the Fuzzy Stability of an Affine Functional Equation

In this paper, we obtain the general solution of the following functional equation f(3x + y + z) + f(x + 3y + z) + f(x + y + 3z) + f(x) + f(y) + f(z) = 6f(x + y + z): We establish the Hyers-Ulam-Rassias stability of the above functional equation in the fuzzy normed spaces. Further we show the above functional equation is stable in the sense of Hyers and Ulam in fuzzy normed spaces.

math.CA↗