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Axioms
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Theory and Application of Integral Inequalities, 2nd Edition
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Theory and Application of Integral Inequalities, 2nd Edition

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 30 April 2026 | Viewed by 1957

Special Issue Editor

Dr. Loredana Ciurdariu

E-Mail Website
Guest Editor
Department of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, Romania
Interests: convex functions; mathematical inequalities; dynamical systems; operator theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Integral inequalities have become increasingly important in the fields of pure mathematics and applied mathematics, garnering more interest from researchers now than in the previous decades. Integral inequalities are closely related to the concept of convexity. The aim of this Special Issue is to expand on the inequalities derived within the framework of q-calculus, fractional calculus, and their generalizations and to identify new types of integral inequalities for various types of convexities. This will contribute to a better understanding and unification of these recently developed theories. The theory of variational inequalities is closely related to convex analysis. The optimality conditions for differentiable convex functions are characterized by variational inequalities. Integral inequalities, particularly Jensen’s inequality, play a crucial role in optimization and information theory, statistics, cryptography,y and many other areas of research. The applications of integral inequalities in operator theory and matrix inequalities are also of significant interest in various areas of pure mathematics. The Guest Editors aim to provide a platform to present the latest advances in various aspects of the theory of integral inequalities and recently developed applications.  

Dr. Loredana Ciurdariu
Guest Editor

Manuscript Submission Information

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Keywords

  • generalized convexity
  • q-calculus
  • fractional calculus
  • variational inequalities
  • interval-valued inequalities
  • Jensen inequality
  • applications in information theory and statistics
  • inequalities related to functions
  • applications of inequalities in operator theory
  • matrix inequality

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Published Papers (5 papers)

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Research

22 pages, 463 KB  
Article
Improved Bounds for Integral Jensen’s Inequality Through Fifth-Order Differentiable Convex Functions and Applications
by Sidra Nisar, Fiza Zafar and Hind Alamri
Axioms 2025, 14(8), 602; https://doi.org/10.3390/axioms14080602 - 2 Aug 2025
Viewed by 363
Abstract
The main objective of this research is to obtain interesting estimates for Jensen’s gap in the integral sense, along with their applications. The convexity of a fifth-order absolute function is used to established proposed estimates of Jensen’s gap. We performed numerical computations to [...] Read more.
The main objective of this research is to obtain interesting estimates for Jensen’s gap in the integral sense, along with their applications. The convexity of a fifth-order absolute function is used to established proposed estimates of Jensen’s gap. We performed numerical computations to compare our estimates with previous findings. With the use of the primary findings, we are able to obtain improvements of the Hölder inequality and Hermite–Hadamard inequality. Furthermore, the primary results lead to some inequalities for power means and quasi-arithmetic means. We conclude by outlining the information theory applications of our primary inequalities. Full article
(This article belongs to the Special Issue Theory and Application of Integral Inequalities, 2nd Edition)
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26 pages, 355 KB  
Article
Extension of an Inequality on Three Intervals and Applications to Csiszár ϕ-Divergence and Landau–Kolmogorov Inequality
by Ðilda Pečarić, Josip Pečarić and Jinyan Miao
Axioms 2025, 14(8), 563; https://doi.org/10.3390/axioms14080563 - 24 Jul 2025
Viewed by 206
Abstract
In this paper, we generalize an inequality for a convex function in one dimension R1 on three intervals to a function with nondecreasing increments in k dimensions Rk on (2n+1) intervals. We prove all the situations [...] Read more.
In this paper, we generalize an inequality for a convex function in one dimension R1 on three intervals to a function with nondecreasing increments in k dimensions Rk on (2n+1) intervals. We prove all the situations when n=1,2 and prove a very special case for a general n as well as the discrete version. The proofs are based on a general conclusion for convex functions, and analogues of this conclusion are established. We apply the discrete case of the inequality to Csiszár ϕ-divergence Iϕ(p,q) in information theory, and the continuous case Iϕ(p1,q1)≤Iϕ(p2,q2) on a measurable set is also established. The same inequality for an ϵ-approximately convex function on a discrete set is also established and can be used to prove a similar Landau–Kolmogorov-type inequality. Full article
(This article belongs to the Special Issue Theory and Application of Integral Inequalities, 2nd Edition)
28 pages, 397 KB  
Article
Hybrid Integral Inequalities on Fractal Set
by Badreddine Meftah, Wedad Saleh, Muhammad Uzair Awan, Loredana Ciurdariu and Abdelghani Lakhdari
Axioms 2025, 14(5), 358; https://doi.org/10.3390/axioms14050358 - 9 May 2025
Viewed by 332
Abstract
In this study, we introduce a new hybrid identity that effectively combines Newton–Cotes and Gauss quadrature, allowing us to recover well-known formulas such as Simpson’s second rule and the left- and right-Radau two-point rules, among others. Building upon this flexible framework, we establish [...] Read more.
In this study, we introduce a new hybrid identity that effectively combines Newton–Cotes and Gauss quadrature, allowing us to recover well-known formulas such as Simpson’s second rule and the left- and right-Radau two-point rules, among others. Building upon this flexible framework, we establish several new biparametrized fractal integral inequalities for functions whose local fractional derivatives are of a generalized convex type. In addition to employing tools from local fractional calculus, our approach utilizes the Hölder inequality, the power mean inequality, and a refined version of the latter. Further results are also derived using the concept of generalized concavity. To support our theoretical findings, we provide a graphical example that illustrates the validity of the obtained results, along with some practical applications that demonstrate their effectiveness. Full article
(This article belongs to the Special Issue Theory and Application of Integral Inequalities, 2nd Edition)
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13 pages, 257 KB  
Article
Investigating the Hyers–Ulam Stability of the Generalized Drygas Functional Equation: New Results and Methods
by Gang Lyu, Yang Liu, Yuanfeng Jin and Yingxiu Jiang
Axioms 2025, 14(4), 315; https://doi.org/10.3390/axioms14040315 - 21 Apr 2025
Viewed by 389
Abstract
In this paper, we explore the Hyers–Ulam stability of a generalized Drygas functional equation, which extends the classical Drygas equation by incorporating additional parameters and conditions. Our investigation focuses on mappings from a real vector space into a Banach space and employs the [...] Read more.
In this paper, we explore the Hyers–Ulam stability of a generalized Drygas functional equation, which extends the classical Drygas equation by incorporating additional parameters and conditions. Our investigation focuses on mappings from a real vector space into a Banach space and employs the fixed-point method to establish stability criteria. Our findings provide new insights into the conditions under which the generalized Drygas equation maintains stability, contributing to the broader understanding of functional equations in mathematical analysis. The results have implications for the study of functional equations and their applications in various mathematical contexts. Full article
(This article belongs to the Special Issue Theory and Application of Integral Inequalities, 2nd Edition)
12 pages, 236 KB  
Article
Spatial Decay Estimates for the Moore–Gibson–Thompson Heat Equation Based on an Integral Differential Inequality
by Naiqiao Qing, Jincheng Shi and Yunfeng Wen
Axioms 2025, 14(4), 265; https://doi.org/10.3390/axioms14040265 - 1 Apr 2025
Viewed by 268
Abstract
The present work investigates the spatial evolution characteristics of solutions to the Moore–Gibson–Thompson heat equation within a three-dimensional cylindrical geometry. By constructing an integral-differential inequality framework, we establish rigorous estimates demonstrating the exponential spatial decay of the solution as the axial distance from [...] Read more.
The present work investigates the spatial evolution characteristics of solutions to the Moore–Gibson–Thompson heat equation within a three-dimensional cylindrical geometry. By constructing an integral-differential inequality framework, we establish rigorous estimates demonstrating the exponential spatial decay of the solution as the axial distance from the inlet boundary increases without bound. This finding aligns with a generalized interpretation of the Saint-Venant principle, demonstrating its applicability under the present asymptotic conditions. The integral-differential inequality method proposed in this paper can also be used for the study of the Saint-Venant principle for other equations. Full article
(This article belongs to the Special Issue Theory and Application of Integral Inequalities, 2nd Edition)
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