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On refinements of some integral inequalities using improved power‐mean integral inequalities
Author(s) -
Kadakal Huriye
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22491
Subject(s) - mathematics , inequality , midpoint , differentiable function , power (physics) , kantorovich inequality , regular polygon , convex function , mean value , hölder's inequality , log sum inequality , mathematical analysis , linear inequality , statistics , geometry , physics , quantum mechanics
In this study, using power‐mean inequality and improved power‐mean integral inequality better approach than power‐mean inequality and an identity for differentiable functions, we get inequalities for functions whose derivatives in absolute value at certain power are convex. Numerically, it is shown that improved power‐mean integral inequality gives better approach than power‐mean inequality. Some applications to special means of real numbers and some error estimates for the midpoint formula are also given.