Open AccessOn a cosine operator function framework of approximation processes in Banach space
Author(s) -
Andi Kivinukk,
Anna Saksa,
Maria Zeltser
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1913213k
Subject(s) - mathematics , trigonometric functions , banach space , operator (biology) , type (biology) , factorization , order (exchange) , discrete cosine transform , pure mathematics , mathematical analysis , algorithm , biochemistry , chemistry , geometry , repressor , transcription factor , gene , ecology , finance , artificial intelligence , biology , computer science , economics , image (mathematics)
We introduce the cosine-type approximation processes in abstract Banach space setting. The historical roots of these processes go back to W. W. Rogosinski in 1926. The given new definitions use a cosine operator functions concept. We proved that in presented setting the cosine-type operators possess the order of approximation, which coincide with results known in trigonometric approximation. Moreover, a general method for factorization of certain linear combinations of cosine operator functions is presented. The given method allows to find the order of approximation using the higher order modulus of continuity. Also applications for the different type of approximations are given.