A Dunkl type generalization of Szász operators via post-quantum calculus

Area of Science:

• Mathematical Analysis
• Approximation Theory
• Post-Quantum Calculus

Background:

• Szász operators are fundamental in approximation theory.
• Post-quantum calculus offers a novel framework for mathematical analysis.
• Dunkl operators generalize classical operators with applications in harmonic analysis.

Purpose of the Study:

• To construct novel Dunkl type Szász operators within the framework of post-quantum calculus.
• To investigate the approximation properties and convergence of these new operators.
• To analyze the rate of convergence for functions in the Lipschitz class and explore bivariate extensions.

Main Methods:

• Construction of Dunkl type Szász operators using post-quantum calculus.
• Application of the modulus of continuity to compute operator convergence.
• Analysis of convergence rates for specific function classes (Lipschitz).
• Extension to bivariate operators.

Main Results:

• Successful construction of Dunkl type Szász operators via post-quantum calculus.
• Demonstration of approximation results and convergence properties.
• Quantification of the rate of convergence for Lipschitz functions.
• Development of the bivariate version of these operators.

Conclusions:

• The newly constructed Dunkl type Szász operators exhibit valuable approximation properties.
• Post-quantum calculus provides a fertile ground for developing generalized operators.
• The study contributes to the understanding of convergence rates for these operators on specific function spaces.