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 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...     

On a Generalization of Szász–Mirakjan–Kantorovich Operators

In this paper we introduce and study a sequence of positive linear operators acting on suitable spaces of measurable functions on [0,+∞[, including L ^p ([0,+∞[) spaces, 1 ≤ p < +∞, as well as continuous function spaces with polynomial weights. These operators generalize the Szász–Mirakjan–Kantorovich operators and they allow to approximate (or to reconstruct) suitable measurable functions by knowing their mean values on a sequence of subintervals of [0,+∞[ that do not constitute a subdivision of it. We also give some estimates of the rates of convergence by means of suitable moduli of smoothness.     

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.     

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.     

Direct,Inverse, and Equivalence Theorems for Weighted Szász—Durrmeyer—Bézier Operators in Orlicz Spaces

Analysis Mathematica - We introduce the Orlicz space corresponding to the Young function and, by virtue of the equivalence theorem between the modified K-functional and modulus of smoothness,...     

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 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 &gt;...     

A Note on the Penrose–Mackay Tiling,HirzbruchSignature of M 4 and Knots in e (∞) Space

Mackays generalization of Penrose tiling is shown to be related to the Hirzbruchsignature, δ, of four manifolds in the case of a Murray–von Neumann continuousdimension in E ^(∞) space. It is further shown that σ is numerically identicalto the Jones knot invariant, V_L, for the right-handed trefoil. Finally, aconjecture regarding the theorem of local isomorphism is presented.     

On Pal Type Weighted Lacunary (0 , 2 ; 0 )-Interpolation on Infinite Interval (?∞, +∞)

In this paper, we study the weighted (0, 2; 0)-interpolation on infinite interval, which means to determine a polynomial of degree 3n–1 when the function values are prescribed at two sets of points namely the zeros of H_n(x) and H_n(x) and the wieghted second derivative at the zeros of H_n(x).