Korovkin Second Theorem via -Statistical -Summability | Zendy

M. ‎Mursaleen | Zendy; Adem Kılıçman | Zendy

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Korovkin Second Theorem via -Statistical -Summability

Author(s) -

M. ‎Mursaleen,

Adem Kılıçman

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/598963

Subject(s) - mathematics , real line , linear operators , sequence (biology) , space (punctuation) , type (biology) , interval (graph theory) , variety (cybernetics) , discrete mathematics , function (biology) , continuous function (set theory) , property (philosophy) , pure mathematics , mathematical analysis , combinatorics , statistics , ecology , linguistics , philosophy , evolutionary biology , biology , bounded function , genetics , epistemology

Korovkin type approximation theorems are useful tools to check whether a given sequence of positive linear operators on of all continuous functions on the real interval is an approximation process. That is, these theorems exhibit a variety of test functions which assure that the approximation property holds on the whole space if it holds for them. Such a property was discovered by Korovkin in 1953 for the functions 1, , and in the space as well as for the functions 1, cos, and sin in the space of all continuous 2-periodic functions on the real line. In this paper, we use the notion of -statistical -summability to prove the Korovkin second approximation theorem. We also study the rate of -statistical -summability of a sequence of positive linear operators defined from into

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