A Dunkl–Type Generalization of Szász–Kantorovich Operators via Post–Quantum Calculus

Abstract

In this paper, we define the ( p , q ) -variant of Szász–Kantorovich operators via Dunkl-type generalization generated by an exponential function and study the Korovkin-type results. We also obtain the convergence of our operators in weighted space by the modulus of continuity, Lipschitz class, and Peetre’s K-functionals. The extra parameter p provides more flexibility in approximation and plays an important role in symmetrizing these newly-defined operators.

Statistically and Relatively Modular Deferred-Weighted Summability and Korovkin-Type Approximation Theorems

“…(31) fairly holds true. Now under condition (31) and by applying Theorem 2, we have that the condition (32) holds true. Moreover, since ( f m,n ) is not relatively modular statistically Cesàro summable, Theorem 1 of Demirci and Orhan (see [31], p. 1173, Theorem 1) does not hold fairly true under the operators considered in (30).…”

“…Very recently, Md. Nasiruzzaman et al [32] proved Dunkl-type generalization of Szász-Kantorovich operators via post-quantum calculus, and consequently, Srivastava et al [33] established the construction of Stancu-type Bernstein operators based on Bézier bases with shape parameter λ.…”

Some Properties of Kantorovich-Stancu-Type Generalization of Szász Operators including Brenke-Type Polynomials via Power Series Summability Method

“…Furthermore, we give a Voronovskaya-type theorem for T − statistical convergence. Such type of operators is widely studied by several authors (see [15][16][17][18][19]).…”

Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces

“…Szász operators [20] provide an extension to Bernstein operators [4] on the interval [0, ∞). In the present years, several authors have studied the Dunkl type generalization of Szász operators (see [1,2,9,10,12,13,[15][16][17]21]).…”