Related papers: Approximation by generalized Szasz operators invol…
This article is the second one of three successive articles of the authors on the matrix-weighted Besov-type and Triebel--Lizorkin-type spaces. In this article, we obtain the sharp boundedness of almost diagonal operators on matrix-weighted…
In this paper, we describe two novel changes to the Baskakov-Durrmeyer operators that improve their approximation performance. These improvements are especially designed to produce higher rates of convergence, with orders of one or two.…
We study various regularization operators on plurisubharmonic functions that preserve Lelong classes with growth given by certain compact convex sets. The purpose is to show that the weighted Siciak-Zakharyuta functions associated with…
In this paper, we introduce a new semi-discrete modulus of smoothness, which generalizes the definition given by Kolomoitsev and Lomako (KL) in 2023 (in the paper published in the J. Approx. Theory), and we establish very general one- and…
This study is an example of a solid connection between fractional analysis and inequality theory, and includes new inequalities of the P\'{o}lya-Szeg% \"{o}-Chebyshev type obtained with the help of Generalized Proportional Fractional…
In this article, we first study, in the framework of operator theory, Pusz and Woronowicz's functional calculus for pairs of bounded positive operators on Hilbert spaces associated with a homogeneous two-variable function on $[0,\infty)^2$.…
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…
This study examines a modified Kantorovich approach applied to generalized sampling series. The paper establishes that the approximation order to a function using these modified operators is atleast as good as that achieved by classical…
Approximation properties of multivariate quasi-projection operators are studied in the paper. Wide classes of such operators are considered, including the sampling and the Kantorovich-Kotelnikov type operators generated by different…
Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…
A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…
The purpose of this paper is to introduce $\omega$-Chebyshev-greedy and $\omega$-partially greedy approximation classes and to study their relation with $\omega$-approximation spaces, where the latter are a generalization of the classical…
By extending the classical quantitative approximation results for positive and linear operators in $L^{p}([0, 1]), 1\le p \le +\infty$ of Berens and DeVore in 1978 and of Swetits and Wood in 1983 to the more general case of sublinear,…
We have developed a generalization of the Zeldovich approximation (ZA) that is exact in a wide variety of situations, including plannar, spherical and cilyndrical symmetries. We have shown that this generalization, that we call complete…
We study weighted Chebyshev polynomials on compact subsets of the complex plane with respect to a bounded weight function. We establish existence and uniqueness of weighted Chebyshev polynomials and derive weighted analogs of Kolmogorov's…
In this paper we investigate the gamma-relative differentiation by the motivation of amending the order of the weighted polynomial approximation on the semiaxis for certain functions. With the help of this we give some definitions of…
In this paper, we analyze the convergence behavior of Hermite-type sampling Kantorovich operators in the context of mixed norm spaces. We prove certain direct approximation theorems, including the uniform convergence theorem, the…
This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of…
In this paper we introduce a general family of Sz\'asz--Mirakjan--Durrmeyer type operators depending on an integer parameter $j \in \mathbb{Z}$. They can be viewed as a generalization of the Sz\'asz--Mirakjan--Durrmeyer operators [9],…
In this article, we analyze the approximation properties of the new family of Durrmeyer type exponential sampling operators. We derive the point-wise and uniform approximation theorem and Voronovskaya type theorem for these generalized…