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New structural properties and Hermite-Hadamard inequalities for Godunova-Levin mappings via a novel analytical approach
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DOI：10.1080/27684830.2025.2574096.png)
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Abstract
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This paper presents new forms of integral inequalities for h-Godunova-Levin mappings defined over various types of quadric surfaces in the Euclidean space & Ropf;n. The first major contribution is the extension of previously known integral inequalities, which were originally formulated on the real line & Ropf;, to higher-dimensional quadric geometries. These generalized results are not only more inclusive but also establish a unified framework that recovers and strengthens several existing inequalities when specific values of ni are chosen for i=1,2and3, corresponding to quadric surfaces in lower-dimensional settings such as & Ropf;, & Ropf;2 and & Ropf;3, where such inequalities have been recently developed. To validate the theoretical advancements, we provide concrete examples of both 2D and 3D surfaces for selected values of n.
Keywords:
Hermite-Hadamard inequality
integral inequalities
Jacobian technique
two-dimensional Godunova-Levin functions
Mathematics subject classification (2010)
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1.1
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72
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