Special Issue "Inequalities II"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: closed (31 October 2020) | Viewed by 6977

Special Issue Editor

Prof. Dr. Shigeru Furuichi
E-Mail Website
Guest Editor
Department of Information Science, College of Humanities and Sciences, Nihon University, 3-25-40, Sakurajyousui, Setagaya-ku, Tokyo 156-8550, Japan
Interests: generalized entropies; inequalities; matrix analysis; operator theory
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Special Issue Information

Dear Colleagues,

This Special Issue is a continuation of the previous successful Special Issue “Inequalities”.

Inequalities often appear in various fields of natural sciences. Nowadays, researchers are still improving and/or generalizing famous classical inequalities. That is, inequalities are being actively studied by mathematicians. Moreover, classical inequalities can be applied in engineering fields, and a newly obtained inequality is beautiful. Such beauty may attract one to the study of inequalities.

In this Special Issue, we call for papers on new results for mathematical inequalities, as well as new proofs for well-known inequalities or short notes with interesting results in open problems. We welcome all kinds of mathematical inequalities, such as scalar inequalities on summation, inequalities on integral form, operator/matrix inequalities, and norm inequalities.

Prof. Dr. Shigeru Furuichi
Guest Editor

Manuscript Submission Information

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Keywords

  • numerical inequalities or geometric inequalities
  • sharpening of inequalities
  • integral/summation inequalities
  • special functions
  • functional inequalities
  • Schur convexity
  • higher-order convexity
  • operator/matrix inequalities
  • norm inequalities
  • rearrangement or majorization
  • singular value inequalities or eigenvalue inequalities
  • Hyers–Ulam stability
  • set-valued mappings

Published Papers (5 papers)

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Research

Article
On the Growth of Higher Order Complex Linear Differential Equations Solutions with Entire and Meromorphic Coefficients
Mathematics 2021, 9(1), 58; https://doi.org/10.3390/math9010058 - 29 Dec 2020
Viewed by 865
Abstract
We revisit the problem of studying the solutions growth order in complex higher order linear differential equations with entire and meromorphic coefficients of p,q-order, proving how it is related to the growth of the coefficient of the unknown function under [...] Read more.
We revisit the problem of studying the solutions growth order in complex higher order linear differential equations with entire and meromorphic coefficients of p,q-order, proving how it is related to the growth of the coefficient of the unknown function under adequate assumptions. Our study improves the previous results due to J. Liu - J. Tu - L. Z Shi, L.M. Li - T.B. Cao, and others. Full article
(This article belongs to the Special Issue Inequalities II)
Article
Weaker Conditions for the q-Steffensen Inequality and Some Related Generalizations
Mathematics 2020, 8(9), 1462; https://doi.org/10.3390/math8091462 - 01 Sep 2020
Cited by 1 | Viewed by 1046
Abstract
The aim of this paper is to study the q-Steffensen inequality and to prove some weaker conditions for this inequality in quantum calculus. Further, we prove q-analogues of some frequently used generalizations of Steffensen’s inequality and obtain some refinements of q [...] Read more.
The aim of this paper is to study the q-Steffensen inequality and to prove some weaker conditions for this inequality in quantum calculus. Further, we prove q-analogues of some frequently used generalizations of Steffensen’s inequality and obtain some refinements of q-Steffensen’s inequality and its generalizations. Full article
(This article belongs to the Special Issue Inequalities II)
Article
New Comparison Theorems for the Nth Order Neutral Differential Equations with Delay Inequalities
Mathematics 2020, 8(3), 454; https://doi.org/10.3390/math8030454 - 22 Mar 2020
Cited by 21 | Viewed by 1654
Abstract
In this work, we present a new technique for the oscillatory properties of solutions of higher-order differential equations. We set new sufficient criteria for oscillation via comparison with higher-order differential inequalities. Moreover, we use the comparison with first-order differential equations. Finally, we provide [...] Read more.
In this work, we present a new technique for the oscillatory properties of solutions of higher-order differential equations. We set new sufficient criteria for oscillation via comparison with higher-order differential inequalities. Moreover, we use the comparison with first-order differential equations. Finally, we provide an example to illustrate the importance of the results. Full article
(This article belongs to the Special Issue Inequalities II)
Article
On a New Half-Discrete Hilbert-Type Inequality Involving the Variable Upper Limit Integral and Partial Sums
Mathematics 2020, 8(2), 229; https://doi.org/10.3390/math8020229 - 10 Feb 2020
Cited by 7 | Viewed by 1309
Abstract
In this paper we establish a new half-discrete Hilbert-type inequality involving the variable upper limit integral and partial sums. As applications, an inequality obtained from the special case of the half-discrete Hilbert-type inequality is further investigated; moreover, the equivalent conditions of the best [...] Read more.
In this paper we establish a new half-discrete Hilbert-type inequality involving the variable upper limit integral and partial sums. As applications, an inequality obtained from the special case of the half-discrete Hilbert-type inequality is further investigated; moreover, the equivalent conditions of the best possible constant factor related to several parameters are proved. Full article
(This article belongs to the Special Issue Inequalities II)
Article
On a New Extended Hardy–Hilbert’s Inequality with Parameters
Mathematics 2020, 8(1), 73; https://doi.org/10.3390/math8010073 - 02 Jan 2020
Cited by 10 | Viewed by 1250
Abstract
In this paper, by introducing parameters and weight functions, with the help of the Euler–Maclaurin summation formula, we establish the extension of Hardy–Hilbert’s inequality and its equivalent forms. The equivalent statements of the best possible constant factor related to several parameters are provided. [...] Read more.
In this paper, by introducing parameters and weight functions, with the help of the Euler–Maclaurin summation formula, we establish the extension of Hardy–Hilbert’s inequality and its equivalent forms. The equivalent statements of the best possible constant factor related to several parameters are provided. The operator expressions and some particular cases are also discussed. Full article
(This article belongs to the Special Issue Inequalities II)
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