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To improve the uniform convergence of the classical Lagrange operators of several variables, we construct a new operator with a class of summation factors. It is proved that the new operator converges...
Let T be the unit circle, f be an \alpha-Holder continuous function on T, \alpha>1/2, and A be the algebra of continuous function in the closed unit disk \bar D that are holomorphic in D. Then f exte...
In this paper, we mainly study the problems of derivative approximation of interpolation polynomials. Based on the zero nodes of the Chebyshev polynomials of the second kind, we construct an interpola...
The shifting operator is applied to generate implicit interpolating equations for curves defined by three and four equidistant data. The equations trade the abscissa of the interpolated point for anot...
In this paper, to improve the uniform convergence of the known Lagrange interpolation polynomials, a new triangle interpolation operator of Bernstein type is constructed by using the method of two rev...
Due to the Lagrange interpolation polynomials do not converge uniformly to arbitrary continuous functions, in this paper, a new interpolation polynomial is constructed by using the weighted average me...
The paper is devoted to the important topic of Fourier analysis in one variable (AMS subject classification 42A16). In this paper we introduce Leindler space of Fourier - Haar coefficients, so we gene...
An interpolation theorem of Donoghue is extended to interpolation of tensor products. The result is related to Korányi's work on monotone matrix functions of several variables.
Interpolation of 2n+k data by spline spaces of order k with n knots is studied. Some conditions on existence of interpolating splines are given. Numerical methods for constructing a solution are sugge...
In the present paper the approximate fuctions for certain multivariate periodic functions with bounded mired derivatives are constructed by making use of their values at the knots of number-theoretica...
Versions of the multiple Nevanlinna-Pick interpolation problem in the class N-circumfiex involving both interior and boundary data are investigated. This leads to solvability criteria for the indicate...
Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in the weighted Lp norm on an arbitrary system of nodes are given.

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