Giaccardi inequality for generalized convex functions and related results

In this article, the famous Giaccardi inequality is generalized for modified ( h , m ) -convex functions under the condition that h is a multiplicative positive function. The results are also discussed for different values of h and m . Also, Lagrange and Cauchy type mean value theorems for the funct...

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Vydané v:Journal of inequalities and applications Ročník 2023; číslo 1; s. 132 - 11
Hlavní autori: Iqbal, Wasim, Rehman, Atiq ur
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 16.10.2023
Springer Nature B.V
SpringerOpen
Predmet:
Analysis
Applications of Mathematics
Control theory
Convex analysis
Differential calculus
Giaccardi inequality
Inequality
Mathematics
Mathematics and Statistics
Modified ( h , m ) $(h,m)$ -convex functions
Modified h-convex functions
Modified
26A51
26D10
convex functions
Giaccardi inequality
26D15
ISSN:1029-242X, 1025-5834, 1029-242X
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Shrnutí:In this article, the famous Giaccardi inequality is generalized for modified ( h , m ) -convex functions under the condition that h is a multiplicative positive function. The results are also discussed for different values of h and m . Also, Lagrange and Cauchy type mean value theorems for the functional due to Giaccardi’s inequality are obtained.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-023-03038-5