Some Estimates On The Hermite-Hadamard Inequality Through Geometrically Quasi-Convex Functions

M. A. Latif; Sever S. Dragomir; E. Momoniat

doi:10.18514/MMN.2017.1819

Some Estimates On The Hermite-Hadamard Inequality Through Geometrically Quasi-Convex Functions

M. A. Latif, Sever S. Dragomir, E. Momoniat

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

In present paper, by proving a new integral identity, using Hölder’s inequality and mathematical analysis, we prove some Hermite-Hadamard type integral inequalities for geometrically quasi-convex functions which give better estimates to those already proven for the rightside of a Hermite-Hadamard type inequality established for geometrically convex functions in earlier works. A numerical example is also provided to support our claim. Applications of the results to special means of positive real numbers are given.

Original language	English
Pages (from-to)	933-946
Number of pages	14
Journal	Miskolc Mathematical Notes
Volume	18
Issue number	2
DOIs	https://doi.org/10.18514/MMN.2017.1819
Publication status	Published - 2017
Externally published	Yes

Keywords

Hermite-Hadamards inequality
Hölder integral inequality
Quasi-Convex functions
convex function
geometrically quasi-convex function

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Numerical Analysis
Discrete Mathematics and Combinatorics
Control and Optimization

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10.18514/MMN.2017.1819

Cite this

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title = "Some Estimates On The Hermite-Hadamard Inequality Through Geometrically Quasi-Convex Functions",

abstract = "In present paper, by proving a new integral identity, using H{\"o}lder{\textquoteright}s inequality and mathematical analysis, we prove some Hermite-Hadamard type integral inequalities for geometrically quasi-convex functions which give better estimates to those already proven for the rightside of a Hermite-Hadamard type inequality established for geometrically convex functions in earlier works. A numerical example is also provided to support our claim. Applications of the results to special means of positive real numbers are given.",

keywords = "Hermite-Hadamards inequality, H{\"o}lder integral inequality, Quasi-Convex functions, convex function, geometrically quasi-convex function",

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note = "Publisher Copyright: {\textcopyright} 2017 Miskolc University Press",

year = "2017",

doi = "10.18514/MMN.2017.1819",

language = "English",

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T1 - Some Estimates On The Hermite-Hadamard Inequality Through Geometrically Quasi-Convex Functions

AU - Latif, M. A.

AU - Dragomir, Sever S.

AU - Momoniat, E.

PY - 2017

Y1 - 2017

N2 - In present paper, by proving a new integral identity, using Hölder’s inequality and mathematical analysis, we prove some Hermite-Hadamard type integral inequalities for geometrically quasi-convex functions which give better estimates to those already proven for the rightside of a Hermite-Hadamard type inequality established for geometrically convex functions in earlier works. A numerical example is also provided to support our claim. Applications of the results to special means of positive real numbers are given.

AB - In present paper, by proving a new integral identity, using Hölder’s inequality and mathematical analysis, we prove some Hermite-Hadamard type integral inequalities for geometrically quasi-convex functions which give better estimates to those already proven for the rightside of a Hermite-Hadamard type inequality established for geometrically convex functions in earlier works. A numerical example is also provided to support our claim. Applications of the results to special means of positive real numbers are given.

KW - Hermite-Hadamards inequality

KW - Hölder integral inequality

KW - Quasi-Convex functions

KW - convex function

KW - geometrically quasi-convex function

UR - https://www.scopus.com/pages/publications/85056379442

U2 - 10.18514/MMN.2017.1819

DO - 10.18514/MMN.2017.1819

M3 - Article

AN - SCOPUS:85056379442

SN - 1787-2405

VL - 18

SP - 933

EP - 946

JO - Miskolc Mathematical Notes

JF - Miskolc Mathematical Notes

IS - 2

ER -

Some Estimates On The Hermite-Hadamard Inequality Through Geometrically Quasi-Convex Functions

Abstract

Keywords

ASJC Scopus subject areas

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