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  • 1. Adeleke, E.
    et al.
    Cizmesija, A.
    Oguntuase, James
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Pokaz, D.
    On a new class of Hardy-type inequalities2012In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2012, no 259Article in journal (Refereed)
    Abstract [en]

    In this paper, we generalize a Hardy-type inequality to the class of arbitrary non-negative functions bounded from below and above with a convex function multiplied with positive real constants. This enables us to obtain new generalizations of the classical integral Hardy's, Hardy-Hilbert's, Hardy-Littlewood-P\'{o}lya's and P\'{o}lya-Knopp's inequalities as well as of Godunova's and of some recently obtained inequalities in multidimensional settings. Finally, we apply a similar idea to functions bounded from below and above with a superquadratic function.

  • 2.
    Kufner, Alois
    et al.
    Mathematical Institute, Academy Sciences of the Czesh Republic.
    Kuliev, K.
    Department of Mathematics, University of West Bohemia.
    Oguntuase, James
    Department of Mathematics, University of Agriculture, Abeokuta.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Generalized weighted inequality with negative powers2007In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 1, no 2, p. 269-280Article in journal (Refereed)
    Abstract [en]

    In this paper necessary and sufficient conditions for the validity of the generalized Hardy inequality for the case -∞ < q p < 0 and 0 < p q < 1 are derived. Furthermore, some special cases are considered

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  • 3.
    Oguntase, James Adedayo
    et al.
    Department of Mathematics, Federal University of Agriculture, Abeokuta.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT The Arctic University of Norway, Narvik.
    Fabulerin, Olanrewaju Olanrewaju
    Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Osun.
    Adeagbo-Sheikh, Abdulaziz G.
    Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Osun.
    Refinements of some limit Hardy-type inequalities via superquadracity2017In: Publications de l'Institut Mathématique (Beograd), ISSN 0350-1302, E-ISSN 1820-7405, Vol. 102, no 116, p. 231-240Article in journal (Refereed)
    Abstract [en]

    Refinements of some limit Hardy-type inequalities are derived anddiscussed using the concept of superquadracity. We also proved that all threeconstants appearing in the refined inequalities obtained are sharp. The naturalturning point of our refined Hardy inequality is 𝑝 = 2 and for this case we haveeven equality.

  • 4.
    Oguntuase, James
    et al.
    Department of Mathematics, Federal University of Agriculture, Abeokuta.
    Fabelurin, Olanrewaju O
    Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Osun.
    Adeagbo-Sheikh, Abdulaziz G
    Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Osun.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Time scale Hardy-type inequalities with ‘broken’ exponent p2015In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2015, article id 2015:17Article in journal (Refereed)
    Abstract [en]

    In this paper, some new Hardy-type inequalities involving ‘broken’ exponents are derived on arbitrary time scales. Our approach uses both convexity and superquadracity arguments, and the results obtained generalize, complement and provide refinements of some known results in literature.

  • 5.
    Oguntuase, James
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics.
    Okopti, Christopher A.
    Department of Mathematics, University of Education, Winneba.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Allotey, Francis K.A.
    Institute of Mathematical Science, Legon-Accra.
    Weighted multidimensional Hardy and Pólya-Knopp's type inequalities2006Report (Other academic)
  • 6.
    Oguntuase, James
    et al.
    Department of Mathematics, University of Agriculture, Abeokuta.
    Okpoti, Christopher A.
    Department of Mathematics, University of Education, Winneba.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Allotey, Francis K.A.
    Institute of Mathemtical Science.
    Multidimensional Hardy type inequalities for p2006Report (Other academic)
  • 7. Oguntuase, James
    et al.
    Okpoti, Christopher
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Allotey, Francis
    Weighted multidimensional Hardy type inequalities via Jensen's inequality2007In: Proceedings of A. Razmadze Mathematical Institute, ISSN 1512-0007, Vol. 144, p. 91-105Article in journal (Refereed)
    Abstract [en]

    The authors prove that Jenson's inequality implies some sharp weighted multidimensional Hardy type inequalities. In particular, their results unify and further extend several results of this type in the literature including the recent results in [A. Čižmešija, J. E. Pečarić and L. E. Persson, J. Approx. Theory 125 (2003), no. 1, 74--84; MR2016841 (2004i:42017); S. Kaijser et al., Math. Inequal. Appl. 8 (2005), no. 3, 403--417; MR2148234 (2006c:26036); S. Kaijser, L. E. Persson and A. Öberg, J. Approx. Theory 117 (2002), no. 1, 140--151; MR1920123 (2003f:26037)]. The main result is obtained in Theorem 3.1. In Section 4, the authors show that some existing results are special cases of the theorems obtained in this paper.

  • 8. Oguntuase, James
    et al.
    Okpoti, Christopher
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Allotey, Francis K.A.
    Institute of Mathematical Science, Legon-Accra.
    Mulitdimensional Hardy type inequalities for p2007In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 1, no 1, p. 1-11Article in journal (Refereed)
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  • 9. Oguntuase, James
    et al.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Hardy type inequalities via convexity: the jouney so far2010In: The Australian Journal of Mathematical Analysis and Applications, ISSN 1449-5910, Vol. 7, no 2, article id 18Article in journal (Refereed)
    Abstract [en]

    It is nowadays well-known that Hardy's inequality (like many other inequalities) follows directly from Jensen's inequality. Most of the development of Hardy type inequalities has not used this simple fact, which obviously was unknown by Hardy himself and many others. Here we report on some results obtained in this way mostly after 2002 by mainly using this fundamental idea.

  • 10. Oguntuase, James
    et al.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Levin-Cochran-Lee type inequalities involving many functions2007In: Proceedings of A. Razmadze Mathematical Institute, ISSN 1512-0007, Vol. 144, p. 107-118Article in journal (Refereed)
  • 11. Oguntuase, James
    et al.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Refinement of Hardy's inequalities via superquadratic and subquadratic functions2008In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 339, no 2, p. 1305-1312Article in journal (Refereed)
    Abstract [en]

    A new refined weighted Hardy inequality for p ≥ 2 is proved and discussed. The inequality is reversed for 1 < p ≤ 2, which means that for p = 2 we have equality. The main tool in the proofs are some new results for superquadratic and subquadratic functions.

  • 12.
    Oguntuase, James
    et al.
    Department of Mathematics, Federal University of Agriculture, Abeokuta.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Time scales Hardy-type inequalities via superquadracity2014In: Annals of Functional Analysis, ISSN 2008-8752, E-ISSN 2008-8752, Vol. 5, no 2, p. 61-73Article in journal (Refereed)
    Abstract [en]

    In this paper some new Hardy-type inequalities on time scales are derived and proved using the concept of superquadratic functions. Also, we extend Hardy-type inequalities involving superquadratic functions with general kernels to the case with arbitrary time scales. Several consequences of our results are given and their connection with recent results in the literature are pointed out and discussed

  • 13. Oguntuase, James
    et al.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Čižmešija, Aleksandra
    University of Zagreb.
    Multidimensional Hardy-type inequalities via convexity2008In: Bulletin of the Australian Mathematical Society, ISSN 0004-9727, E-ISSN 1755-1633, Vol. 77, no 2, p. 245-260Article in journal (Refereed)
    Abstract [en]

    Let an almost everywhere positive function Φ be convex for p>1 and p<0, concave for p∈(0,1), and such that Axp≤Φ(x) ≤Bxp holds on ℝ+ for some positive constants A≤B. In this paper we derive a class of general integral multidimensional Hardy-type inequalities with power weights, whose left-hand sides involve Φ (∫0x1⋯∫0xnf(t) dt) instead of [(∫0x1⋯∫0xnf(t) dt]p, while the corresponding right-hand sides remain as in the classical Hardy's inequality and have explicit constants in front of integrals. We also prove the related dual inequalities. The relations obtained are new even for the one-dimensional case and they unify and extend several inequalities of Hardy type known in the literature.

  • 14. Oguntuase, James
    et al.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Essel, Emmanuel Kwame
    Multidimensional Hardy-type inequalities with general kernels2008In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 348, no 1, p. 411-418Article in journal (Refereed)
    Abstract [en]

    Some new multidimensional Hardy-type inequalities involving arithmetic mean operators with general positive kernels are derived. Our approach is mainly to use a convexity argument and the results obtained improve some known results in the literature and, in particular, some recent results in [S. Kaijser, L. Nikolova, L.-E. Persson, A. Wedestig, Hardy-type inequalities via convexity, Math. Inequal. Appl. 8 (3) (2005) 403-417] are generalized and complemented.

  • 15. Oguntuase, James
    et al.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Essel, Emmanuel Kwame
    Popoola, B.A.
    Department of Mathematics and Statistics, University of Cape Coast.
    Refined multidimensional Hardy-type inequalities via superquadracity2008In: Banach Journal of Mathematical Analysis, ISSN 1735-8787, Vol. 2, no 2, p. 129-139Article in journal (Refereed)
    Abstract [en]

    Some new refined multidimensional Hardy-type inequalities for p 2 and their duals are derived and discussed. Moreover, these inequalities hold in the reversed direction when 1 < p 2. The results obtained are based mainly on some new results for superquadratic and subquadratic functions. In particular, our results further extend the recent results in [J.A. Oguntuase and L.-E. Persson, Refinement of Hardy's inequalities via superquadratic and subquadratic functions, J

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  • 16. Oguntuase, James
    et al.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Pecaric, J.
    Some remarks on a result of Bougoffa2010In: The Australian Journal of Mathematical Analysis and Applications, ISSN 1449-5910, Vol. 7, no 2, article id 60Article in journal (Refereed)
  • 17.
    Oguntuase, James
    et al.
    Department of Mathematics, University of Agriculture, Abeokuta.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some Hardy type inequalities with "broken" exponent p2014In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 8, no 3, p. 405-416Article in journal (Refereed)
    Abstract [en]

    Some new Hardy-type inequalities, where the parameter p is permitted to take different values in different intervals, are proved and discussed. The parameter can even be negative in one interval and greater than one in another. Moreover, a similar result is derived for a multidimensional case.

  • 18. Oguntuase, James
    et al.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Sonubi, A.
    Federal University of Agriculture, Abeokuta, Ogun State.
    On the equivalence between some multidimensional Hardy-type inequalities2014In: Banach Journal of Mathematical Analysis, ISSN 1735-8787, Vol. 8, no 1Article in journal (Refereed)
    Abstract [en]

    We prove and discuss some power weighted Hardy-type inequalities on finite and infinite sets. In particular, it is proved that these inequalities are equivalent because they can all be reduced to an elementary inequality, which can be proved by Jensen inequality. Moreover, the corresponding limit (Pólya-Knopp type) inequalities and equivalence theorem are proved. All constants in these inequalities are sharp.

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  • 19.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Oguntuase, James
    Refinement of Hardy's inequality for "all" p.2008In: Proceedings of the 2nd international symposium on Banach and function spaces II (ISBFS 2006),: Kitakyushu, Japan, September 14-17, 2006 / [ed] Mikio Kato; Lech Maligranda, Yokohama: Yokohama Publishers, 2008, p. 129-144Conference paper (Refereed)
1 - 19 of 19
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