Approximation of functions by bivariate q-Stancu-Durrmeyer type operators

This paper is in continuation of our work in [24], wherein we studied someapproximation properties of the Stancu-Durrmeyer operators based on q-integers. Here,we construct a bivariate generalization of these operators and study the rate of convergenceby means of the complete modulus of continuity and the partial moduli of continuity andthe degree of approximation with the aid of the Peetre\u27s K functional. Subsequently, wedene the GBS(Generalized Boolean Sum) operators of Stancu- Durrmeyer type and givethe rate of approximation by means of the mixed modulus of smoothness and the Lipschitzclass of Bogel-continuous functions

Recent progress on univariate and multivariate polynomial and spline quasi-interpolants

Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to solve), uniform boundedness independently of the degree (polynomials) or of the partition (splines), good approximation order. We shall emphasize new results on various types of univariate and multivariate polynomial or spline QIs, depending on the nature of coefficient functionals, which can be differential, discrete or integral. We shall also present some applications of QIs to numerical methods

GENERALIZED BERNSTEIN-KANTOROVICH OPERATORS OF BLENDING TYPE

In this note, we derive some approximation properties of the generalized Bernstein-Kantorovich type operators based on two nonnegative parameters considered  by A. Kajla [Appl. Math. Comput. 2018]. We establish Voronovskaja type asymptotic theorem for these operators. The rate of convergence for differential functions whose derivatives are of bounded variation is also derived. Finally, we show the convergence of the operators by illustrative graphics in Mathematica software to certain functions

Approximation properties of Stancu type Szász-Mirakjan operators

In this paper, a class of Stancu type Szász-Mirakjan operators are introduced. The approximation properties of the operators are discussed using tools of modulus of continuity, modulus of smoothness and K-functional. The estimation of the Lipschitz function class by the operators is also studied. Later, the Voronvskaya type asymptotic expansion of the operators is established. Finally, we compare the convergence of these newly defined operators for certain functions with certain graphs

Polynomials: Special Polynomials and Number-Theoretical Applications

Polynomials play a crucial role in many areas of mathematics including algebra, analysis, number theory, and probability theory. They also appear in physics, chemistry, and economics. Especially extensively studied are certain infinite families of polynomials. Here, we only mention some examples: Bernoulli, Euler, Gegenbauer, trigonometric, and orthogonal polynomials and their generalizations. There are several approaches to these classical mathematical objects. This Special Issue presents nine high quality research papers by leading researchers in this field. I hope the reading of this work will be useful for the new generation of mathematicians and for experienced researchers as wel