Advances in Convex Analysis and Inequalities

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 30 September 2025 | Viewed by 246

Special Issue Editor


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Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 050711 Bucharest, Romania
Interests: operations research; risk management; mathematics of finance; optimization theory; nonlinear functional analysis; differential equations; real analysis; numerical analysis
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Special Issue Information

Dear Colleagues,

Convex analysis, a vital branch of mathematics, explores the properties of convex functions and sets, providing crucial tools and applications across various scientific and mathematical disciplines. Its significance is particularly notable in optimization problems, where convex functions offer several advantageous properties. Additionally, inequalities such as Jensen's and Hermite–Hadamard inequalities, which are essential in convex functions, play a pivotal role in many mathematical areas.

This Special Issue welcomes submissions on new developments in convex analysis and mathematical inequalities, including innovative proofs of classical inequalities and their generalizations. We welcome contributions across various domains, such as integral, differential, norm, operator, and matrix inequalities, as well as applications in probability and statistics. We encourage the submission of papers on new proofs of well-known inequalities or inequalities in various domains: integral inequalities, differential inequalities, and norm, operator, and matrix inequalities.

Dr. Marius Radulescu
Guest Editor

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Keywords

  • convex analysis
  • convex optimization
  • convex functions
  • biconvex functions
  • generalized convexity
  • majorization theory
  • Schur convex functions
  • Jensen inequality
  • Hermite–Hadamard inequality
  • weighted inequalities
  • geometric inequalities
  • variational inequalities
  • equilibrium problems

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Published Papers (1 paper)

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Research

14 pages, 264 KiB  
Article
An Improved Version of the Parameterized Hardy–Hilbert Inequality Involving Two Partial Sums
by Bicheng Yang and Shanhe Wu
Mathematics 2025, 13(8), 1331; https://doi.org/10.3390/math13081331 - 18 Apr 2025
Viewed by 115
Abstract
In this paper, by employing the Euler–Maclaurin summation formula and real analysis techniques, an improved version of the parameterized Hardy–Hilbert inequality involving two partial sums is established. Based on the obtained inequality, the equivalent conditions of the best possible constant factor related to [...] Read more.
In this paper, by employing the Euler–Maclaurin summation formula and real analysis techniques, an improved version of the parameterized Hardy–Hilbert inequality involving two partial sums is established. Based on the obtained inequality, the equivalent conditions of the best possible constant factor related to several parameters are discussed. Our results extend the classical Hardy–Hilbert inequality and improve certain existing results. Full article
(This article belongs to the Special Issue Advances in Convex Analysis and Inequalities)
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