October 17, 2025Open Access

On a generalized Pachpatte inequality through a convexity-based approach

CCChristophe ChesneauMarathwada Agricultural University

Key Points

The extension of the Pachpatte inequality introduces a new dimension to integral inequalities, enhancing flexibility.
By employing a general convex function, this approach broadens the applicability of the original methods.
Several examples illustrate the theory, showcasing the innovative techniques resulting from the new framework.
This work not only expands on past inequalities but also invites further development in analytical methods.

Abstract

In this article, we extend a key integral inequality established by Pachpatte in 2002 by introducing a new convexity-based approach. Specifically, we incorporate a general convex function to create a flexible framework that can be adapted to various mathematical contexts. The resulting techniques are original and reusable, offering potential for further innovations in related analytical frameworks. We present several examples to illustrate the theory and demonstrate the versatility of the approach.

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