Reşat Aslan - Provincial Directorate of Labor and Employment Agency, 63050, Şanlıurfa, Turkey. Aydin Izgi - Department of Mathematics, Faculty of Sciences and Arts, Harran University, 63100, Şanlıurfa, Turkey.
In this work, we obtain the approximation properties of a new generalization of Szász-Mirakjan operators based on post-quantum calculus. Firstly, for these operators, a recurrence formulation for the moments is obtained, and up to the fourth degree, the central moments are examined. Then, a local approximation result is attained. Furthermore, the degree of approximation in respect of the modulus of continuity on a finite closed set and the class of Lipschitz are computed. Next, the weighted uniform approximation on an unbounded interval is showed, and by the modulus of continuity, the order of convergence is estimated. Lastly, we proved the Voronovskaya type theorem and gave some illustrations to compare the related operators' convergence to a certain function.
Reşat Aslan, Aydin Izgi, Approximation by a new generalization of Szász-Mirakjan operators via \((p,q)\)-calculus, Journal of Nonlinear Sciences and Applications, 14 (2021), no. 5, 310--323
Aslan Reşat, Izgi Aydin, Approximation by a new generalization of Szász-Mirakjan operators via \((p,q)\)-calculus. J. Nonlinear Sci. Appl. (2021); 14(5):310--323
Aslan, Reşat, Izgi, Aydin. "Approximation by a new generalization of Szász-Mirakjan operators via \((p,q)\)-calculus." Journal of Nonlinear Sciences and Applications, 14, no. 5 (2021): 310--323
