On two inequalities of Čebyšev

2016/09/20 by Mohammad W. Alomari, Alomari, Mohammad W.
Computer Science · Mathematics · #26A15 #26A51 #26D10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1609.06232

openalex publication_date 2016/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, several sharp bounds for the Čebyšev functional involving various type of functions are proved. In particular, for the Čebyšev functional of two absolutely continuous functions whose first derivatives are both convex, convex and belong to L_p-spaces, convex and bounded variation, convex and Lipschitz mappings new sharp bounds are presented. Other related results regarding two convex and concave functions are given.

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