On reverse Hölder and Minkowski inequalities
-
Chang-Jian Zhao
und
Wing Sum Cheung
Abstract
In the paper, we give new improvements of the reverse Hölder and Minkowski integral inequalities. These new results in special case yield the Pólya-Szegö’s inequality and reverse Minkowski’s inequality, respectively.
This work was supported by National Natural Science Foundation of China Grant No. 10971205, 11371334.
(Communicated by Tomasz Natkaniec)
References
[1] Bechenbach, E. F.—Bellman, R.: Inequalities, Springer-Verlag, Berlin-Göttingen, Heidelberg, 1961.10.1007/978-3-642-64971-4Suche in Google Scholar
[2] Dragomir, S. S.: Asupra unor inegalităţi, Caiete Metodico-Şiinţifice, Matematica 13, Univ. Timisoara, 1984.Suche in Google Scholar
[3] Dragomir, S. S.—Khan, L.: Two discrete inequalities of Grüss type via Pólya-Szegö and Shisha-Mond results for real numbers, Tamkang J. Math. 35 (2004), 117–128.10.5556/j.tkjm.35.2004.213Suche in Google Scholar
[4] Hardy, G. H.—Littlewood, J. E.—Pólya, G.: Inequalities, Cambridge Univ. Press, Cambridge, 1934.Suche in Google Scholar
[5] Liu, X. H.: On reverse Hölder inequality, Math. Pract. Theory 1990 (1990), 84–88.Suche in Google Scholar
[6] Mitrinović, D. S.: Analytic Inequalities, Springer-Verlag Berlin, Heidelberg, New York, 1970.10.1007/978-3-642-99970-3Suche in Google Scholar
[7] Pólya, G.—Szegö, G.: Aufgaben und Lehrsätze aus der Analysis I, Berlin, 1925, p. 57 and 213–214.10.1007/978-3-662-38381-0Suche in Google Scholar
[8] Wang, C.-L.: On development of inverses of Cauchy and Hölder inequalities, SIAM Review. 21 (1979), 550–557.10.1137/1021096Suche in Google Scholar
[9] Wu, S. H.: Generalization of a sharp Hölder’s inequality and its application, J. Math. Anal. Appl. 332 (2007), 741–750.10.1016/j.jmaa.2006.10.019Suche in Google Scholar
[10] Wu, S. H.: A new sharpened and generalized version of Hölder’s inequality and its applications, Appl. Math. Comput. 197 (2008), 708–714.10.1016/j.amc.2007.08.006Suche in Google Scholar
[11] Wu, S. H.: Some improvements of Aczél’s inequality and Popoviciu’s inequality, Computers. Math. Appl. 56 (2008), 1196–1205.10.1016/j.camwa.2008.02.021Suche in Google Scholar
[12] Yang, S. G.: Reverse Minkowski inequality and its applications, J. Tongling College 13 (2002), 71–76.Suche in Google Scholar
[13] Zhao, C.-J.—Cheung, W. S.: On Pólya-Szegö’s inequality, J. Inequal. Appl. 2013 (2013), #591.10.1186/1029-242X-2013-591Suche in Google Scholar
© 2020 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Regular papers
- Some relative normality properties in locales
- Upper bounds of some special zeros for the Rankin-Selberg L-function
- Factorization of polynomials over valued fields based on graded polynomials
- Varieties of ∗-regular rings
- On reverse Hölder and Minkowski inequalities
- Coefficient inequalities related with typically real functions
- Existence of wandering and periodic domain in given angular region
- The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*
- Uniqueness problem of meromorphic mappings of a complete Kähler manifold into a projective space
- Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces
- Bn-maximal operator and Bn-singular integral operators on variable exponent Lebesgue spaces
- 𝔻-recurrent ∗-Ricci tensor on three-dimensional real hypersurfaces in nonflat complex space forms
- More on closed non-vanishing ideals in CB(X)
- The Lindley negative-binomial distribution: Properties, estimation and applications to lifetime data
- Multi-opponent James functions
- An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications
- A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models
- On the bond pricing partial differential equation in a convergence model of interest rates with stochastic correlation
- Characterization of linear mappings on (Banach) ⋆-algebras by similar properties to derivations
Artikel in diesem Heft
- Regular papers
- Some relative normality properties in locales
- Upper bounds of some special zeros for the Rankin-Selberg L-function
- Factorization of polynomials over valued fields based on graded polynomials
- Varieties of ∗-regular rings
- On reverse Hölder and Minkowski inequalities
- Coefficient inequalities related with typically real functions
- Existence of wandering and periodic domain in given angular region
- The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*
- Uniqueness problem of meromorphic mappings of a complete Kähler manifold into a projective space
- Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces
- Bn-maximal operator and Bn-singular integral operators on variable exponent Lebesgue spaces
- 𝔻-recurrent ∗-Ricci tensor on three-dimensional real hypersurfaces in nonflat complex space forms
- More on closed non-vanishing ideals in CB(X)
- The Lindley negative-binomial distribution: Properties, estimation and applications to lifetime data
- Multi-opponent James functions
- An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications
- A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models
- On the bond pricing partial differential equation in a convergence model of interest rates with stochastic correlation
- Characterization of linear mappings on (Banach) ⋆-algebras by similar properties to derivations
