Related papers: Approximation by Kantorovich type (p,q)-Bernstein-…
The $\alpha$-Bernstein operators were initially introduced in the paper by Chen, X., Tan, J., Liu, Z., Xie, J. (2017) titled "Approximation of Functions by a New Family of Generalized Bernstein Operators" (Journal of Mathematical Analysis…
In this paper, the behavior of the sampling Kantorovich operators has been studied, when discontinuous signals are considered in the above sampling series. Moreover, the rate of approximation for the family of the above operators is…
In this paper we introduce and study a new sequence of positive linear operators acting on function spaces defined on a convex compact subset. Their construction depends on a given Markov operator, a positive real number and a sequence of…
In this paper multivariate extension of the generalized Durrmeyer sampling type series are considered. We establish a Voronovskaja type formula and a quantitative version. Finally some particular examples are discussed.
This deals with the Stancu variant of (p, q)-Sz\'asz-Mirakyan-Baskakov operators. Estimation of moments and establishing few basic approximation results which comprise weighted approximation and direct estimates in view of modulus of…
Herein we propose a complex form of a genuine Bernstein-Durrmeyer type operators depending on a non-negative real parameter $\alpha.$ We present the quantitative upper bound, Voronovskaja type result and exact order of approximation for…
Positive polynomial operator that approximates Urison operator, when integration domain is a "regular triangle" is investigated. We obtain Bernstein Polynomials as a particular case.
In the present article, we introduce a $(p,q)$-analogue of the poly-Euler polynomials and numbers by using the $(p,q)$-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We give…
In this paper, we introduce a new sequence of operators based on the Gr\"unwald interpolation operators on Chebyshev nodes on the space $L^p[0,{\pi}]$. The operators we consider are integral variants of the Gr\"unwald interpolation…
In this paper, we provide a unifying theory concerning the convergence properties of the so-called max-product Kantorovich sampling operators based upon generalized kernels in the setting of Orlicz spaces. The approximation of functions…
In the present paper, the new generalized classes of (p,q)-starlike and $(p,q)$-convex functions are introduced by using the (p,q)-derivative operator. Also, the (p,q)-Bernardi integral operator for analytic function is defined in an open…
In this paper, we construct a Durrmeyer-type variant of Gr\"unwald interpolation operators on the space $L^p[0,{\pi}]$. We prove their fundamental properties, including boundedness and convergence in the $L^p$-norm. We establish the…
Artificial neural network operators (ANNOs) have been widely used for approximating deterministic input-output functions; however, their extension to random dynamics remains comparatively unexplored. In this paper, we construct a new class…
The Bernstein operators allow to build recursively the Schur functions. We present a recursion formula for k-Schur functions at t=1 based on combinatorial operators that generalize the Bernstein operators. The recursion leads immediately to…
The present article deals with the local approximation results by means of Lipschitz maximal function, Ditzian-Totik modulus of smoothness and Lipschitz type space having two parameters for the summation-integral type operators defined by…
We study approximation of multivariate periodic functions from Besov and Triebel--Lizorkin spaces of dominating mixed smoothness by the Smolyak algorithm constructed using a special class of quasi-interpolation operators of…
We study the class of $(p,q)$-regular operators between quasi-Banach lattices. In particular, a representation of this class as the dual of a certain tensor norm for Banach lattices is given. We also provide some factorization results for…
We consider the pointwise weighted approximation by Bernstein operators with inner singularities. The related weight functions are weights $\bar{w}(x)=|x-\xi|^\alpha(0<\xi<1,\ \alpha>0).$ In this paper we give direct and inverse results of…
In this paper we prove Korovkin type theorem for iterates of general positive linear operators $T:C\left[ 0,1\right] \rightarrow C\left[ 0,1\right] $ and derive quantitative estimates in terms of modulus of smoothness. In particular, we…
In this paper, we introduce Mellin-Steklov exponential samplingoperators of order $r,r\in\mathbb{N}$, by considering appropriate Mellin-Steklov integrals. We investigate the approximation properties of these operators in continuousbounded…