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Keywords = reverse Minkowski integral inequality

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23 pages, 504 KB  
Article
Fractional Reverse Inequalities Involving Generic Interval-Valued Convex Functions and Applications
by Bandar Bin-Mohsin, Muhammad Zakria Javed, Muhammad Uzair Awan, Badreddine Meftah and Artion Kashuri
Fractal Fract. 2024, 8(10), 587; https://doi.org/10.3390/fractalfract8100587 - 3 Oct 2024
Cited by 9 | Viewed by 1749
Abstract
The relation between fractional calculus and convexity significantly impacts the development of the theory of integral inequalities. In this paper, we explore the reverse of Minkowski and Hölder’s inequality, unified Jensen’s inequality, and Hermite–Hadamard (H-H)-like inequalities using fractional calculus [...] Read more.
The relation between fractional calculus and convexity significantly impacts the development of the theory of integral inequalities. In this paper, we explore the reverse of Minkowski and Hölder’s inequality, unified Jensen’s inequality, and Hermite–Hadamard (H-H)-like inequalities using fractional calculus and a generic class of interval-valued convexity. We introduce the concept of I.V-(,) generic class of convexity, which unifies several existing definitions of convexity. By utilizing Riemann–Liouville (R-L) fractional operators and I.V-(,) convexity to derive new improvements of the H-H- and Fejer and Pachpatte-like inequalities. Our results are quite unified; by substituting the different values of parameters, we obtain a blend of new and existing inequalities. These results are fruitful for establishing bounds for I.V R-L integral operators. Furthermore, we discuss various implications of our findings, along with numerical examples and simulations to enhance the reliability of our results. Full article
(This article belongs to the Special Issue Fractional Integral Inequalities and Applications, 3rd Edition)
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12 pages, 275 KB  
Article
Inequalities in Riemann–Lebesgue Integrability
by Anca Croitoru, Alina Gavriluţ, Alina Iosif and Anna Rita Sambucini
Mathematics 2024, 12(1), 49; https://doi.org/10.3390/math12010049 - 22 Dec 2023
Cited by 2 | Viewed by 1654
Abstract
In this paper, we prove some inequalities for Riemann–Lebesgue integrable functions when the considered integration is obtained via a non-additive measure, including the reverse Hölder inequality and the reverse Minkowski inequality. Then, we generalize these inequalities to the framework of a multivalued case, [...] Read more.
In this paper, we prove some inequalities for Riemann–Lebesgue integrable functions when the considered integration is obtained via a non-additive measure, including the reverse Hölder inequality and the reverse Minkowski inequality. Then, we generalize these inequalities to the framework of a multivalued case, in particular for Riemann–Lebesgue integrable interval-valued multifunctions, and obtain some inequalities, such as a Minkowski-type inequality, a Beckenbach-type inequality and some generalizations of Hölder inequalities. Full article
27 pages, 474 KB  
Article
Certain New Reverse Hölder- and Minkowski-Type Inequalities for Modified Unified Generalized Fractional Integral Operators with Extended Unified Mittag–Leffler Functions
by Wengui Yang
Fractal Fract. 2023, 7(8), 613; https://doi.org/10.3390/fractalfract7080613 - 9 Aug 2023
Cited by 6 | Viewed by 1714
Abstract
In this article, we obtain certain novel reverse Hölder- and Minkowski-type inequalities for modified unified generalized fractional integral operators (FIOs) with extended unified Mittag–Leffler functions (MLFs). The predominant results of this article generalize and extend the existing fractional Hölder- and Minkowski-type integral inequalities [...] Read more.
In this article, we obtain certain novel reverse Hölder- and Minkowski-type inequalities for modified unified generalized fractional integral operators (FIOs) with extended unified Mittag–Leffler functions (MLFs). The predominant results of this article generalize and extend the existing fractional Hölder- and Minkowski-type integral inequalities in the literature. As applications, the reverse versions of weighted Radon-, Jensen- and power mean-type inequalities for modified unified generalized FIOs with extended unified MLFs are also investigated. Full article
(This article belongs to the Special Issue Mathematical Inequalities in Fractional Calculus and Applications)
26 pages, 401 KB  
Article
Results on Minkowski-Type Inequalities for Weighted Fractional Integral Operators
by Hari Mohan Srivastava, Soubhagya Kumar Sahoo, Pshtiwan Othman Mohammed, Artion Kashuri and Nejmeddine Chorfi
Symmetry 2023, 15(8), 1522; https://doi.org/10.3390/sym15081522 - 2 Aug 2023
Cited by 9 | Viewed by 2397
Abstract
This article considers a general family of weighted fractional integral operators and utilizes this general operator to establish numerous reverse Minkowski inequalities. When it comes to understanding and investigating convexity and inequality, symmetry is crucial. It provides insightful explanations, clearer explanations, and useful [...] Read more.
This article considers a general family of weighted fractional integral operators and utilizes this general operator to establish numerous reverse Minkowski inequalities. When it comes to understanding and investigating convexity and inequality, symmetry is crucial. It provides insightful explanations, clearer explanations, and useful methods to help with the learning of key mathematical ideas. The kernel of the general family of weighted fractional integral operators is related to a wide variety of extensions and generalizations of the Mittag-Leffler function and the Hurwitz-Lerch zeta function. It delves into the applications of fractional-order integral and derivative operators in mathematical and engineering sciences. Furthermore, this article derives specific cases for selected functions and presents various applications to illustrate the obtained results. Additionally, novel applications involving the Digamma function are introduced. Full article
(This article belongs to the Special Issue Asymmetric and Symmetric Study on Number Theory and Cryptography)
16 pages, 318 KB  
Article
Local Fractional Integral Hölder-Type Inequalities and Some Related Results
by Guangsheng Chen, Jiansuo Liang, Hari M. Srivastava and Chao Lv
Fractal Fract. 2022, 6(4), 195; https://doi.org/10.3390/fractalfract6040195 - 31 Mar 2022
Cited by 17 | Viewed by 2568
Abstract
This paper is devoted to establishing some functional generalizations of Hölder and reverse Hölder’s inequalities with local fractional integral introduced by Yang. Then, based on the obtained results, we derive some related inequalities including local fractional integral Minkowski-type and Dresher-type inequalities, which are [...] Read more.
This paper is devoted to establishing some functional generalizations of Hölder and reverse Hölder’s inequalities with local fractional integral introduced by Yang. Then, based on the obtained results, we derive some related inequalities including local fractional integral Minkowski-type and Dresher-type inequalities, which are some extensions of several existing local fractional integral inequalities. Full article
20 pages, 351 KB  
Article
Reverse Minkowski Inequalities Pertaining to New Weighted Generalized Fractional Integral Operators
by Rozana Liko, Pshtiwan Othman Mohammed, Artion Kashuri and Y. S. Hamed
Fractal Fract. 2022, 6(3), 131; https://doi.org/10.3390/fractalfract6030131 - 24 Feb 2022
Cited by 8 | Viewed by 2698
Abstract
In this paper, we obtain reverse Minkowski inequalities pertaining to new weighted generalized fractional integral operators. Moreover, we derive several important special cases for suitable choices of functions. In order to demonstrate the efficiency of our main results, we offer many concrete examples [...] Read more.
In this paper, we obtain reverse Minkowski inequalities pertaining to new weighted generalized fractional integral operators. Moreover, we derive several important special cases for suitable choices of functions. In order to demonstrate the efficiency of our main results, we offer many concrete examples as applications. Full article
(This article belongs to the Special Issue Fractional Integral Inequalities and Applications)
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