On Two Kinds of the Hardy-Type Integral Inequalities in the Whole Plane with the Equivalent Forms

Book chapter

Yang, B., Andrica, D., Bagdasar, O. and Rassias, M.T. 2021. On Two Kinds of the Hardy-Type Integral Inequalities in the Whole Plane with the Equivalent Forms. in: Ioannis N. Parasidis, Efthimios Providas and Themistocles M. Rassias (ed.) Mathematical Analysis in Interdisciplinary Research Springer. pp. 1025 - 1048
AuthorsYang, B., Andrica, D., Bagdasar, O. and Rassias, M.T.
EditorsIoannis N. Parasidis, Efthimios Providas and Themistocles M. Rassias
Abstract

By the use of weight functions, a few equivalent conditions of two kinds of Hardy-type integral inequalities with multi-parameters in the whole plane are obtained. The constant factors related to the extended Riemann-zeta function are proved to be the best possible. Applying our results, we deduce a few equivalent conditions of two kinds of Hardy-type integral inequalities in the whole plane and some particular cases.

KeywordsBest constants; ; Equivalent form; ; Hardy-type integral inequality; ; Parameter; ; Riemann-zeta function; ; Weight function
Page range 1025 - 1048
Year2021
Book titleMathematical Analysis in Interdisciplinary Research
PublisherSpringer
Edition1st
SeriesSpringer Optimization and Its Applications
ISBN978-3-030-84721-0
978-3-030-84723-4
978-3-030-84720-3
ISSN1931-6836
Digital Object Identifier (DOI)https://doi.org/10.1007/978-3-030-84721-0_39
Web address (URL)http://www.scopus.com/inward/record.url?eid=2-s2.0-85126667076&partnerID=MN8TOARS
https://link.springer.com/book/10.1007/978-3-030-84721-0
Output statusPublished
Publication dates2021
12 Mar 2023
11 Mar 2022
Online11 Mar 2022
Online10 Mar 2022
Publication process dates
Deposited25 May 2023
JournalSpringer Optimization and Its Applications
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Bagdasar, Ovidiu, Popovici, Nicolae and Bagdasar, O. 2017. LOCAL MAXIMIZERS OF GENERALIZED CONVEX VECTOR-VALUED FUNCTIONS. Journal of Nonlinear and Convex Analysis.
On the number of complex horadam sequences with a fixed period
Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the number of complex horadam sequences with a fixed period. Fibonacci Quarterly.
On the characterization of periodic complex Horadam sequences
Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the characterization of periodic complex Horadam sequences. Fibonacci Quarterly.
On a result of Bunder involving Horadam sequences: A proof and generalization
Larcombe, Peter J. and Bagdasar, Ovidiu 2013. On a result of Bunder involving Horadam sequences: A proof and generalization. Fibonacci Quarterly.
Influence discovery in semantic networks: An initial approach
Trovati, M. and Bagdasar, O. 2014. Influence discovery in semantic networks: An initial approach. IEEE. https://doi.org/10.1109/uksim.2014.48
Complementary iInequalities involving the Stolarsky Mean
Bagdasar, Ovidiu 2010. Complementary iInequalities involving the Stolarsky Mean. Journal of Inequalities and Applications. https://doi.org/10.1155/2010/492570
Concise computer mathematics: tutorials on theory and problems
Bagdasar, Ovidiu 2013. Concise computer mathematics: tutorials on theory and problems. Springer.
On the characterization of periodic generalized Horadam sequences
Bagdasar, Ovidiu and Larcombe, Peter J. 2014. On the characterization of periodic generalized Horadam sequences. Journal of Difference Equations and Applications. https://doi.org/10.1080/10236198.2014.891022
Local maximum points of explicitly quasiconvex functions
Bagdasar, Ovidiu and Popovici, Nicolae 2014. Local maximum points of explicitly quasiconvex functions. Optimization Letters. https://doi.org/10.1007/s11590-014-0781-3
A horadam-based pseudo-random number generator
Bagdasar, O.D., Chen, M. and Bagdasar, O. 2014. A horadam-based pseudo-random number generator. IEEE. https://doi.org/10.1109/uksim.2014.55
On the structure of periodic complex Horadam orbits
Bagdasar, Ovidiu D., Larcombe, Peter J., Anjum, Ashiq and Bagdasar, O. 2016. On the structure of periodic complex Horadam orbits. Carpathian Journal of Mathematics.
Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems
Popa, I.-L., Ceauşu, T., Bagdasar, O. and Agarwal, R.P. 2016. Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems. Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica. 27 (2), pp. 153-166. https://doi.org/10.2478/auom-2019-0025
On some functions involving the lcm and gcd of integer tuples
Bagdasar, Ovidiu 2014. On some functions involving the lcm and gcd of integer tuples. Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics. https://doi.org/10.5937/SPSUNP1402091B
ON A RESULT OF BUNDER INVOLVING HORADAM SEQUENCES: A NEW PROOF
Larcombe, Peter J., Bagdasar, O. and Fennessey, Eric J. 2014. ON A RESULT OF BUNDER INVOLVING HORADAM SEQUENCES: A NEW PROOF. Fibonacci Quarterly. pp. 175-177.