Generalization of cyclic refinements of Jensen’s inequality by Fink’s identity

We generalize cyclic refinements of Jensen’s inequality from a convex function to a higher-order convex function by means of Lagrange–Green’s function and Fink’s identity. We formulate the monotonicity of the linear functionals obtained from these identities utilizing the theory of inequalities for n-convex functions at a point. New Grüss- and Ostrowski-type bounds are found for identities associated with the obtained inequalities. Finally, we investigate the properties of linear functionals regarding exponential convexity and mean value theorems. © 2018, The Author(s).

Авторы
Mehmood N.1 , Butt S.I.1 , Horváth L.2 , Pečarić J. 3, 4
Редакторы
-
Издательство
Springer International Publishing
Номер выпуска
-
Язык
Английский
Страницы
-
Статус
Опубликовано
Подразделение
-
Номер
51
Том
2018
Год
2018
Организации
  • 1 Department of Mathematics, COMSATS, Institute of Information Technology, Lahore, Pakistan
  • 2 Department of Mathematics, University of Pannonia, Veszprém, Hungary
  • 3 Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia
  • 4 RUDN University, Moscow, Russian Federation
Ключевые слова
Convex function; Fink’s identity; Green function; Grüss and Ostrowski inequality; n-Convex function at a point; Čebyšev functional
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/7297/