Some new Hermite–Hadamard type inequalities for s-convex functions and their applications

In this paper, we establish some new integral inequalities of Hermite–Hadamard type for s -convex functions by using the Hölder–İşcan integral inequality. We also compare our new results with the known results and show that the results which we obtained are better than the known results. Finally, we...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2019; no. 1; pp. 1 - 11
Main Authors Özcan, Serap, İşcan, İmdat
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 17.07.2019
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Convex analysis
Convex function
Hermite–Hadamard type inequality
Hölder inequality
Hölder–İşcan inequality
Inequalities
Integral inequalities
Integrals
Mathematics
Mathematics and Statistics
s-convex function
Trapezoidal formula
26A51
Special means
Convex function
Hölder inequality
Integral inequalities
26D15
Hermite–Hadamard type inequality
Hölder–İşcan inequality
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Summary:In this paper, we establish some new integral inequalities of Hermite–Hadamard type for s -convex functions by using the Hölder–İşcan integral inequality. We also compare our new results with the known results and show that the results which we obtained are better than the known results. Finally, we give some applications to trapezoidal formula and to special means.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-019-2151-2