On the Generalized Szász–Mirakyan Operators

In this paper, we construct sequences of Szász–Mirakyan operators which are based on a function ρ. This function not only characterizes the operators but also characterizes the Korovkin set ${\left \{ 1,\rho ,\rho ^{2} \right \}}$ in a weighted function space. We give theorems about convergence of these operators to the identity operator on weighted spaces which are constructed using the function ρ and which are subspaces of the space of continuous functions on ${\mathbb{R} ^{+}}$ . We give quantitative type theorems in order to obtain the degree of weighted convergence with the help of a weighted modulus of continuity constructed using the function ρ. Further, we prove some shape-preserving properties of the operators such as the ρ-convexity and the monotonicity. Our results generalize the corresponding ones for the classical Szász operators.     

Approximation of some Feller semigroups associated with a modification of Szász–Mirakjan–Kantorovich operators

We deepen the study of a sequence (C _n ) _n≧1 of positive linear operators, first introduced in [4], that generalize the classical Szász–Mirakjan–Kantorovich operators. In particular, we present some qualitative properties and an asymptotic formula for such a sequence. Moreover, we prove that, under suitable assumptions, the C ₀-semigroups generated by the second order differential operator $$V_l(u)(x)=xu''(x)+\frac{l}{2} u'(x)\quad (x \geqq 0,\ l \in [0, 2]) $$ on suitable domains of continuous or integrable functions may be approximated by means of iterates of the C _n ’s.     

On certain q-analogue of Sz��sz Kantorovich operators

In the present paper we propose q-analogue of the well known Sz??sz-Kantorovich operators. We study local approximation as well as weighted approximation properties of these new operators.     

Stancu Type Generalization of Dunkl Analogue of Szàsz Operators

In this paper, we introduce Stancu type generalization of Dunkl analogue of Szàsz operators. We obtain some direct results, which include asymptotic formula and error estimation in terms of of the modulus continuity. Also, we investigate the convergence of these operators in a weighted space and estimate the rate of convergence.     

Approximation by the Complex form of a Link Operator Between the Phillips and the Szász–Mirakjan Operators

Results in Mathematics - The link operator $${P_{\alpha}^\rho(f,x)=\sum_{k=1}^\infty s_{\alpha,k}(x)\int_0^\infty \theta_{\alpha,k}^\rho(t)f(t)dt+e^{-\alpha x}f(0)}$$ , $${\alpha, \rho >...     

On q-Parametric Szász-Mirakjan Operators

In the present paper, we introduce q-parametric Szász-Mirakjan operators. We study convergence properties of these operators S _n,q (f). We obtain inequalities for the weighted approximation error of q-Szász-Mirakjan operators. Such inequalities are valid for functions of polynomial growth and are expressed in terms of weighted moduli of continuity. We also discuss Voronovskaja-type formula for q-Szász-Mirakjan operators.     

Simultaneous approximation by Szász–Mirakjan–Stancu–Durrmeyer type operators

In this paper, the study of the problem of simultaneous approximation by the Szász–Mirakjan–Stancu–Durrmeyer type operators is carried out. An upper bound for the approximation to the rth-derivative of a function by these operators is established.     

Direct estimates of the weighted simultaneous approximation by the Szász–Mirakjan operator

Periodica Mathematica Hungarica - We establish direct estimates of the rate of weighted simultaneous approximation by the Szász–Mirakjan operator for smooth functions in the supremum...     

Quantitative Estimates for Generalized Szász Operators of Max-Product Kind

We introduce a certain type generalized Szász operators of max-product kind and give an upper estimate for the error of approximation using a Shisha–Mond-type theorem.     

On Baskakov–Szász–Mirakyan-type operators preserving exponential type functions

The current article deals with the study of Baskakov–Szász–Mirakyan operators which reproduces constant and exponential functions. We discuss a uniform estimate and establish a quantitative result for the modified operators.     

On a class of Szász-Mirakyan type operators

The actual construction of the Szász-Mirakyan operators and its various modifications require estimations of infinite series which in a certain sense restrict their usefulness from the computational point of view. Thus the question arises whether the Szász-Mirakyan operators and their generalizations cannot be replaced by a finite sum. In connection with this question we propose a new family of linear positive operators.     

A note on Szász–Mirakyan–Kantorovich type operators preserving $$e^{-x}$$

In the present article, we study modified form of Szász–Mirakyan–Kantorovich operators, which reproduce constant and \(e^{-x}\) functions. We discuss a uniform convergence result along with a quantitative estimate for the modified operators.     

Approximation by Complex q-Szász–Kantorovich Operators in Compact Disks, q>1

In this paper, the exact order $\frac{1}{q^{n}}, q>1$ , in approximation and Voronovskaja-type results for the complex $q$ -Szász–Kantorovich operators attached to analytic functions on compact disks are obtained.     

Approximation properties of Szász–Mirakyan operators preserving exponential functions

Positivity - This paper is a natural continuation of Acar et al. (Mediterr J Math 14:6, 2017, https://doi.org/10.1007/s00009-016-0804-7 ) where Szász–Mirakyan operators preserving...     

Note on Szász–Mirakyan–Durrmeyer Operators Preserving e2ax,a>0

In the current article, we study Szász–Mirakyan–Durrmeyer operators which reproduces constant and e^2ax,a>0 functions. We discuss a uniform estimate and estimate a quantitative asymptotic formula for the modified operators.