Year: 2025
Type: article
Abstract: We establish an integral representation for Popoviciu’s convex functions of d variables. This representation serves as a foundation for deriving several functional inequalities, analogous to those well-known for usual convex functions. Our results generalize and extend the results obtained by S. Gal, C. Niculescu, B. Gavrea, T. Popoviciu, and others, who considered only differentiable functions of two variables. In contrast to other authors, we do not impose any additional regularity assumptions on the studied functions.
Source: Results in Mathematics
Authors: Andrzej Komisarski, Teresa Rajba
Institutions: University of Łódź, University of Bielsko-Biała
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4411325530