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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Published in:	Journal of inequalities and applications Vol. 2023; no. 1; pp. 132 - 11
Main Authors:	Iqbal, Wasim, Rehman, Atiq ur
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 16.10.2023 Springer Nature B.V SpringerOpen
Subjects:	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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Abstract	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.
AbstractList	Abstract In this article, the famous Giaccardi inequality is generalized for modified ( h , m ) $(h,m)$ -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. 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. 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. In this article, the famous Giaccardi inequality is generalized for modified $(h,m)$ ( 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.
ArticleNumber	132
Author	Rehman, Atiq ur Iqbal, Wasim
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Snippet	In this article, the famous Giaccardi inequality is generalized for modified ( h , m ) -convex functions under the condition that h is a multiplicative... In this article, the famous Giaccardi inequality is generalized for modified $(h,m)$ ( h , m ) -convex functions under the condition that h is a multiplicative... In this article, the famous Giaccardi inequality is generalized for modified (h,m)-convex functions under the condition that h is a multiplicative positive... Abstract In this article, the famous Giaccardi inequality is generalized for modified ( h , m ) $(h,m)$ -convex functions under the condition that h is a...
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SubjectTerms	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
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Title	Giaccardi inequality for generalized convex functions and related results
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