A note on generalized convex functions

In the article, we provide an example for a η -convex function defined on rectangle is not convex, prove that every η -convex function defined on rectangle is coordinate η -convex and its converse is not true in general, define the coordinate ( η 1 , η 2 ) -convex function and establish its Hermite–...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2019; no. 1; pp. 1 - 10
Main Authors Zaheer Ullah, Syed, Adil Khan, Muhammad, Chu, Yu-Ming
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 12.11.2019
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Convex function
Coordinate ( η 1 , η 2 ) $(\eta _{1}, \eta _{2})$ -convex function
Coordinate convex function
Goal programming
Mathematics
Mathematics and Statistics
η-convex function
39B62
Coordinate convex function
Convex function
26A51
Coordinate
26D15
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Summary:In the article, we provide an example for a η -convex function defined on rectangle is not convex, prove that every η -convex function defined on rectangle is coordinate η -convex and its converse is not true in general, define the coordinate ( η 1 , η 2 ) -convex function and establish its Hermite–Hadamard type inequality.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-019-2242-0