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Approximation of the Jensen Gap for First Order Differentiable Functions

Year: 2025

Type: article

Abstract: This article proposes two upper bounds for the gap of discrete and integral Jensen inequality for the functions f ∈ C[a, b]. First bound is obtained when |f′|q , q > 1 is convex and second is obtained when this function is concave. In the convex case, an example is discussed to authenticate the bound when |f′| is not convex. Accordingly and consequently, bounds for the gap of celebrated Hermite-Hadamard and well-known Hölder inequalities are deduced. Also, some estimates for the quasi-arithmetic and power means, and for some basic divergences are obtained from the main results.

Source: Contemporary Mathematics

DOI: 10.37256/cm.6520257588

Authors: Tareq Saeed, Muhammad Adil Khan, Asma Bibi, Shahid Khan, Yu-Ming Chu

Institutions: King Abdulaziz University, University of Peshawar, Government of Khyber Pakhtunkhwa, Hangzhou Normal University

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4413805634

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