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A note on the modified Picard integral operators
Author(s) -
Yılmaz Başar,
Aydın Arı Didem
Publication year - 2021
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.6360
Subject(s) - mathematics , smoothness , modulus of continuity , exponential function , continuation , convergence (economics) , pure mathematics , operator theory , mathematical analysis , type (biology) , ecology , computer science , economics , biology , programming language , economic growth
This study is a natural continuation of modified Picard operators, defined by Agratini et al, preserving an exponential function. Herein, we first show that these operators are approximation processes in the setting of large classes of weighted spaces. Then, we obtain weighted uniform convergence of the operators via exponential weighted modulus of smoothness. Finally, we give, by using the weighted modulus of continuity, the result regarding global smoothness preservation properties for the generalized Picard operators, which based in Agratini et al.