Vaibhav Sharma’s research while affiliated with Netaji Subhas University of Technology and other places

In the present paper, we study the approximation properties of the compositions of Jain operators and Szász–Mirakjan operators. First, we estimate the moment-generating function and moments of the new operators in terms of the Lambert W function and then we establish some convergence results and their quantitative estimates for the difference of the operators, while emphasizing on the preservation of the modulus of continuity. We further discuss Korovkin-type theorem using a Chebyshev system of exponential functions and Voronovskaja-type asymptotic formulae for these operators. In the last section, we provide a comparative study of the rates of convergence of these operators using graphs and numerical tables.

In the present article, we examine the approximation properties of certain Gamma-type operators. Precisely, we consider the compositions of Rathore and Lupaş operators. We estimate the moments of the new composition operators and provide their probabilistic interpretation as well. Then, we provide some convergence results and their difference estimates, while focusing on the preservation of the moduli of smoothness of first- and second-order, using a stochastic approach. Additionally, Korovkin-type theorems and Voronovskaja-type asymptotic formulas are established for these operators. Finally, we consider graphical examples and their numerical interpretations to compare the speed of convergence for the composition operators and their components.

In this article, we study the approximation properties of Durrmeyer-type sampling operators. We consider the composition of generalized sampling operators and Durrmeyer sampling operators. For the new composition operators, we provide the pointwise and uniform convergence, as well as the quantitative estimates in terms of the first-order modulus of continuity and K-functional. Moreover, we investigate the rate of convergence using weighted modulus of continuity. Also, difference estimates are provided for the operators. Additionally, we provide approximation results for the linear combinations of the composition operators. Finally, we discuss the rate of convergence for the operators via graphical example.

In this paper, we address a discrete operator based on the composition of Ismail–May operator and Szász–Mirakjan operator and study its approximation properties for various classes of continuous functions using Taylor's formula. We estimate its moments and further give direct theorems employing Peetre's K‐functional and the modulus of continuity. Furthermore, Voronovskaja‐type asymptotic theorems are given. Additionally, we provide further compositions and give a comparison among their approximation properties.

In the present article, we introduce a Durrmeyer variant of certain approximation operators. We estimate the moment-generating function and moments of these operators employing the Lambert W function and establish some direct results. We further provide a composition of these operators with Szász–Mirakjan operators and estimate direct results for the composition operator. Additionally, we provide a graphical comparison of the approximation properties of the operators.