On Willett's, Godunova--Levin's, and Rozanova's Opial-Type Inequalities with Related Stolarsky-Type Means
Matematičeskie zametki, Tome 96 (2014) no. 6, pp. 803-819
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In this paper, we consider generalizations of Opial's inequality due to Willett, Godunova, Levin, and Rozanova. Cauchy-type mean-value theorems are proved and used in studying Stolarsky-type means defined by the obtained inequalities. Also, a method of producing $n$-exponentially convex and exponentially convex functions is applied.
Keywords:
Willett's inequality, Godunova–Levin's inequality, Rozanova's inequality, Cauchy mean-value theorems, exponential convexity, Stolarsky means.
@article{MZM_2014_96_6_a0,
author = {M. Andric and A. Barbir and J. Pe\v{c}ari\'c},
title = {On {Willett's,} {Godunova--Levin's,} and {Rozanova's} {Opial-Type} {Inequalities} with {Related} {Stolarsky-Type} {Means}},
journal = {Matemati\v{c}eskie zametki},
pages = {803--819},
publisher = {mathdoc},
volume = {96},
number = {6},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a0/}
}
TY - JOUR AU - M. Andric AU - A. Barbir AU - J. Pečarić TI - On Willett's, Godunova--Levin's, and Rozanova's Opial-Type Inequalities with Related Stolarsky-Type Means JO - Matematičeskie zametki PY - 2014 SP - 803 EP - 819 VL - 96 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a0/ LA - ru ID - MZM_2014_96_6_a0 ER -
%0 Journal Article %A M. Andric %A A. Barbir %A J. Pečarić %T On Willett's, Godunova--Levin's, and Rozanova's Opial-Type Inequalities with Related Stolarsky-Type Means %J Matematičeskie zametki %D 2014 %P 803-819 %V 96 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a0/ %G ru %F MZM_2014_96_6_a0
M. Andric; A. Barbir; J. Pečarić. On Willett's, Godunova--Levin's, and Rozanova's Opial-Type Inequalities with Related Stolarsky-Type Means. Matematičeskie zametki, Tome 96 (2014) no. 6, pp. 803-819. http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a0/