Open AccessOn the first derivative of the sums of trigonometric series with quasi-convex coefficients of higher order
Author(s) -
Xhevat Z. Krasniqi
Publication year - 2010
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.276
H-Index - 6
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2010.14.06
Subject(s) - mathematics , series (stratigraphy) , quasiconvex function , trigonometric series , sine , order (exchange) , trigonometric functions , representation (politics) , mathematical analysis , regular polygon , trigonometry , convex analysis , convex optimization , geometry , paleontology , finance , politics , political science , law , economics , biology
In this paper, for the sum of sine or cosine series with quasiconvex coefficients of higher order, the representation of their first derivatives are found in terms of the r-th differences of coefficients of the series obtained by formal differentiation. Also some estimates in terms of coefficients of the series are obtained for the integrals of the absolute values of those derivatives.