Giaccardi Inequality for Modified <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>h</mi> </math>-Convex Functions and Mean Value Theorems

Yonghong Liu, Nadeem Iqbal, Atiq Ur Rehman, Ghulam Farid, Kamsing Nonlaopon

Type: Article

Publication Date: 2022-07-04

Citations: 0

DOI: https://doi.org/10.1155/2022/4364886

Abstract

In this article, we consider the class of modified <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>h</mi> <mo>−</mo> </math> convex functions and derive the famous Giaccardi and Petrovi <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <msup> <mrow> <mtext>c</mtext> </mrow> <mrow> <mo>′</mo> </mrow> </msup> </math> type inequalities for this class of functions. The mean value theorems for the functionals due to Giaccardi and Petrovi <math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"> <msup> <mrow> <mtext>c</mtext> </mrow> <mrow> <mo>′</mo> </mrow> </msup> </math> type inequalities are formulated. Some special cases are discussed by taking different examples of function <math xmlns="http://www.w3.org/1998/Math/MathML" id="M5"> <mi>h</mi> </math> .

Locations

Journal of Function Spaces - View - PDF
DOAJ (DOAJ: Directory of Open Access Journals) - View

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