On generalization of refinement of Jensen’s inequality using Fink’s identity and Abel-Gontscharoff Green function

In this paper, we formulate new Abel-Gontscharoff type identities involving new Green functions for the ‘two-point right focal’ problem. We use Fink’s identity and a new Abel-Gontscharoff-type Green’s function for a ‘two-point right focal’ to generalize the refinement of Jensen’s inequality given in (Horváth and Pečarić in Math. Inequal. Appl. 14: 777-791, 2011) from convex function to higher order convex function. Also we formulate the monotonicity of the linear functional obtained from these identities using the recent theory of inequalities for n-convex function at a point. Further we give the bounds for the identities related to the generalization of the refinement of Jensen’s inequality using inequalities for the Cebyšev functional. Some results relating to the Grüss and Ostrowski-type inequalities are constructed. © 2017, The Author(s).

Авторы
Niaz T.1 , Khan K.A.1 , Pečarić J. 2
Редакторы
-
Издательство
Springer International Publishing
Номер выпуска
-
Язык
Английский
Страницы
-
Статус
Опубликовано
Подразделение
-
Номер
254
Том
2017
Год
2017
Организации
  • 1 Department of Mathematics, University of Sargodha, Sargodha, 40100, Pakistan
  • 2 RUDN University, Miklukho-Maklaya str. 6, 117198, Moscow, Russian Federation
Ключевые слова
Abel-Gontscharoff interpolating polynomial; convex function; Fink’s identity; Green function for ‘two-point right focal’ problem; Jensen’s inequality
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5984/