Open AccessGeneralization of Szász operators: quantitative estimate and bounded variation
Author(s) -
K. Bozkurt,
Mohamed Lemine Limmam,
Ali Aral
Publication year - 2021
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.13.3.775-789
Subject(s) - mathematics , bounded variation , variation (astronomy) , generalization , bounded function , modulus of continuity , exponential type , exponential function , convergence (economics) , order (exchange) , type (biology) , space (punctuation) , function (biology) , operator theory , pure mathematics , mathematical analysis , computer science , ecology , physics , finance , evolutionary biology , astrophysics , economics , biology , economic growth , operating system
Difference of exponential type Szász and Szász-Kantorovich operators is obtained. Similar estimates are given for higher order $\mu$-derivatives of the Szász operators and the Szász-Kantorovich type operators acting on the same order $\mu$-derivative of the function. These differences are given in quantitative form using first modulus of continuity. Convergence in variation of the operators in the space of functions with bounded variation with respect to the variation seminorm is obtained. The results propose a general framework covering the results provided by previous literature.