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Quantum (q, h)-Bézier surfaces based on bivariate (q, h)-blossoming

Jegdić Ilija, Simeonov Plamen, Zafiris Vasilis

Demonstratio Mathematica

2019

Vol. 52, nr 1

451--466

We introduce the (q, h)-blossom of bivariate polynomials, and we define the bivariate (q, h)-Bernstein polynomials and (q, h)-Bézier surfaces on rectangular domains using the tensor product. Usingthe (q, h)-blossom, we construct recursive evaluation algorithms for (q, h)-Bézier surfaces and we derive adual functional property, a Marsden identity, and a number of other properties for bivariate (q, h)-Bernsteinpolynomials and (q, h)-Bézier surfaces. We develop a subdivision algorithm for (q, h)-Bézier surfaces witha geometric rate of convergence. Recursive evaluation algorithms for quantum (q, h)-partial derivatives ofbivariate polynomials are also derived.

New results on the q-generalized Bernoulli polynomials of level m

Urieles Alejandro, Ortega María José, Ramírez William, Vega Samuel

Demonstratio Mathematica

2019

Vol. 52, nr 1

511--522

This paper aims to show new algebraic properties from the q-generalized Bernoulli polynomials [wzór] of level m, as well as some others identities which connect this polynomial class with the q-generalized Bernoulli polynomials of level m, as well as the q-gamma function, and the q-Stirling numbersof the second kind and the q-Bernstein polynomials.

A new approach for solving Bratu’s problem

Ghomanjani Fateme, Shateyi Stanford

Demonstratio Mathematica

2019

Vol. 52, nr 1

336--346

A numerical technique for one-dimensional Bratu’s problem is displayed in this work. The technique depends on Bernstein polynomial approximation. Numerical examples are exhibited to verify the efficiency and accuracy of the proposed technique. In this sequel, the obtained error was shown between the proposed technique, Chebyshev wavelets, and Legendre wavelets. The results display that this technique is accurate.

on q-Baskakov type operators

Aral A., Gupta V.

Demonstratio Mathematica

2009

Vol. 42, nr 1

109-122

In the present paper we introduce two q-analogous of the well known Baskakoy operators. For the first operator we obtain convergence property on bounded interval. Then we give the montonity on the sequence of q-Baskakov operators for n when the function f is convex. For second operator, we obtain direct approximation property on unbounded interval and estimate the rate of convergence. One can say that, depending on the selection of q, these operators are more flexible then the classical Baskakov operators while retaining their approximation properties.

Inverse theorem in simultaneous approximation by Micchelli combination of Bernstein polynomials

Agrawal P.

Demonstratio Mathematica

1998

Vol. 31, nr 1

55-62

The present paper is a continuation of our work [1]. Here we have studied the inverse theorem