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Approximation properties of the Post‐Widder operators preserving e 2 a x , a > 0
Author(s) -
Sofyalıoğlu Melek,
Kanat Kadir
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6192
Subject(s) - mathematics , modulus of continuity , convergence (economics) , constant coefficients , constant (computer programming) , function (biology) , rate of convergence , type (biology) , operator theory , mathematical analysis , pure mathematics , computer science , ecology , channel (broadcasting) , computer network , evolutionary biology , economics , biology , programming language , economic growth
This paper deals with constructing the modified form of the Post‐Widder operators, which reproduce constant ande 2 a xfor fixed a > 0 . We discuss the uniform convergence of the constructed operators with the function f . We illustrate the convergence behaviour of the new operators with the selected function f . After that, we investigate the rate of convergence by using different types of the modulus of continuity and deal with a quantitative Voronovskaya‐type theorem. Finally, we compare our new constructed operators with Post‐Widder operators preservingx r , r ∈ N .