Special Issue "Inequalities"

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

Deadline for manuscript submissions: 31 August 2019

Special Issue Editor

Guest Editor
Prof. Dr. Shigeru Furuichi

Department of Information Science, College of Humanities and Sciences, Nihon University, 3-25-40, Sakurajyousui, Setagaya-ku, Tokyo, 156-8550, Japan
Website | E-Mail
Interests: inequality; entropy; operator/matrix; matrix analysis; mathematical physics and information theory

Special Issue Information

Dear Colleagues,

Inequalities often appear in various fields of natural sciences. Nowadays, famous classical inequalities are still improved and/or generalized by many researchers. That is, inequalities have been actively studied by mathematicians. Moreover, classical inequalities can be applied to engineering fields, while 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 (9 papers)

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Research

Open AccessArticle
Hermite-Hadamard Type Inequalities for Interval (h1, h2)-Convex Functions
Mathematics 2019, 7(5), 436; https://doi.org/10.3390/math7050436
Received: 18 April 2019 / Revised: 13 May 2019 / Accepted: 14 May 2019 / Published: 17 May 2019
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Abstract
We introduce the concept of interval (h1,h2)-convex functions. Under the new concept, we establish some new interval Hermite-Hadamard type inequalities, which generalize those in the literature. Also, we give some interesting examples. [...] Read more.
We introduce the concept of interval ( h 1 , h 2 ) -convex functions. Under the new concept, we establish some new interval Hermite-Hadamard type inequalities, which generalize those in the literature. Also, we give some interesting examples. Full article
(This article belongs to the Special Issue Inequalities)
Open AccessArticle
Generalized Steffensen’s Inequality by Fink’s Identity
Mathematics 2019, 7(4), 329; https://doi.org/10.3390/math7040329
Received: 11 February 2019 / Revised: 27 March 2019 / Accepted: 28 March 2019 / Published: 4 April 2019
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Abstract
By using Fink’s Identity, Green functions, and Montgomery identities we prove some identities related to Steffensen’s inequality. Under the assumptions of n-convexity and n-concavity, we give new generalizations of Steffensen’s inequality and its reverse. Generalizations of some inequalities (and their reverse), [...] Read more.
By using Fink’s Identity, Green functions, and Montgomery identities we prove some identities related to Steffensen’s inequality. Under the assumptions of n-convexity and n-concavity, we give new generalizations of Steffensen’s inequality and its reverse. Generalizations of some inequalities (and their reverse), which are related to Hardy-type inequality. New bounds of Gr u ¨ ss and Ostrowski-type inequalities have been proved. Moreover, we formulate generalized Steffensen’s-type linear functionals and prove their monotonicity for the generalized class of ( n + 1 ) -convex functions at a point. At the end, we present some applications of our study to the theory of exponentially convex functions. Full article
(This article belongs to the Special Issue Inequalities)
Open AccessArticle
New Integral Inequalities via the Katugampola Fractional Integrals for Functions Whose Second Derivatives Are Strongly η-Convex
Mathematics 2019, 7(2), 183; https://doi.org/10.3390/math7020183
Received: 28 December 2018 / Revised: 3 February 2019 / Accepted: 12 February 2019 / Published: 15 February 2019
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Abstract
In this paper, we introduced some new integral inequalities of the Hermite–Hadamard type for functions whose second derivatives in absolute values at certain powers are strongly η -convex functions via the Katugampola fractional integrals. Full article
(This article belongs to the Special Issue Inequalities)
Open AccessArticle
Some Quantum Estimates of Hermite-Hadamard Inequalities for Quasi-Convex Functions
Mathematics 2019, 7(2), 152; https://doi.org/10.3390/math7020152
Received: 18 December 2018 / Revised: 22 January 2019 / Accepted: 2 February 2019 / Published: 5 February 2019
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Abstract
In this paper, we develop some quantum estimates of Hermite-Hadamard type inequalities for quasi-convex functions. In some special cases, these quantum estimates reduce to the known results. Full article
(This article belongs to the Special Issue Inequalities)
Open AccessArticle
More on Inequalities for Weaving Frames in Hilbert Spaces
Mathematics 2019, 7(2), 141; https://doi.org/10.3390/math7020141
Received: 14 January 2019 / Revised: 29 January 2019 / Accepted: 30 January 2019 / Published: 2 February 2019
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Abstract
In this paper, we present several new inequalities for weaving frames in Hilbert spaces from the point of view of operator theory, which are related to a linear bounded operator induced by three Bessel sequences and a scalar in the set of real [...] Read more.
In this paper, we present several new inequalities for weaving frames in Hilbert spaces from the point of view of operator theory, which are related to a linear bounded operator induced by three Bessel sequences and a scalar in the set of real numbers. It is indicated that our results are more general and cover the corresponding results recently obtained by Li and Leng. We also give a triangle inequality for weaving frames in Hilbert spaces, which is structurally different from previous ones. Full article
(This article belongs to the Special Issue Inequalities)
Open AccessArticle
New Refinement of the Operator Kantorovich Inequality
Mathematics 2019, 7(2), 139; https://doi.org/10.3390/math7020139
Received: 7 December 2018 / Revised: 21 January 2019 / Accepted: 24 January 2019 / Published: 1 February 2019
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Abstract
We focus on the improvement of operator Kantorovich type inequalities. Among the consequences, we improve the main result of the paper [H.R. Moradi, I.H. Gümüş, Z. Heydarbeygi, A glimpse at the operator Kantorovich inequality, Linear Multilinear Algebra, doi:10.1080/03081087.2018.1441799]. Full article
(This article belongs to the Special Issue Inequalities)
Open AccessArticle
Coefficient Inequalities of Functions Associated with Hyperbolic Domains
Mathematics 2019, 7(1), 88; https://doi.org/10.3390/math7010088
Received: 4 December 2018 / Revised: 4 January 2019 / Accepted: 8 January 2019 / Published: 16 January 2019
Cited by 1 | PDF Full-text (273 KB) | HTML Full-text | XML Full-text
Abstract
In this work, our focus is to study the Fekete-Szegö functional in a different and innovative manner, and to do this we find its upper bound for certain analytic functions which give hyperbolic regions as image domain. The upper bounds obtained in this [...] Read more.
In this work, our focus is to study the Fekete-Szegö functional in a different and innovative manner, and to do this we find its upper bound for certain analytic functions which give hyperbolic regions as image domain. The upper bounds obtained in this paper give refinement of already known results. Moreover, we extend our work by calculating similar problems for the inverse functions of these certain analytic functions for the sake of completeness. Full article
(This article belongs to the Special Issue Inequalities)
Open AccessArticle
Some Inequalities for g-Frames in Hilbert C*-Modules
Mathematics 2019, 7(1), 25; https://doi.org/10.3390/math7010025
Received: 8 November 2018 / Revised: 25 December 2018 / Accepted: 26 December 2018 / Published: 27 December 2018
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Abstract
In this paper, we obtain new inequalities for g-frames in Hilbert C*-modules by using operator theory methods, which are related to a scalar λR and an adjointable operator with respect to two g-Bessel sequences. It is demonstrated that our [...] Read more.
In this paper, we obtain new inequalities for g-frames in Hilbert C * -modules by using operator theory methods, which are related to a scalar λ R and an adjointable operator with respect to two g-Bessel sequences. It is demonstrated that our results can lead to several known results on this topic when suitable scalars and g-Bessel sequences are chosen. Full article
(This article belongs to the Special Issue Inequalities)
Open AccessArticle
Coefficient Inequalities of Functions Associated with Petal Type Domains
Mathematics 2018, 6(12), 298; https://doi.org/10.3390/math6120298
Received: 13 November 2018 / Revised: 30 November 2018 / Accepted: 1 December 2018 / Published: 3 December 2018
Cited by 1 | PDF Full-text (276 KB) | HTML Full-text | XML Full-text
Abstract
In the theory of analytic and univalent functions, coefficients of functions’ Taylor series representation and their related functional inequalities are of major interest and how they estimate functions’ growth in their specified domains. One of the important and useful functional inequalities is the [...] Read more.
In the theory of analytic and univalent functions, coefficients of functions’ Taylor series representation and their related functional inequalities are of major interest and how they estimate functions’ growth in their specified domains. One of the important and useful functional inequalities is the Fekete-Szegö inequality. In this work, we aim to analyze the Fekete-Szegö functional and to find its upper bound for certain analytic functions which give parabolic and petal type regions as image domains. Coefficient inequalities and the Fekete-Szegö inequality of inverse functions to these certain analytic functions are also established in this work. Full article
(This article belongs to the Special Issue Inequalities)
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