Sanja Varošanec Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, Zagreb, Croatia

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We present generalizations of the Pinelis extension of Stolarsky’s inequality and its reverse. In particular, a new Stolarsky-type inequality is obtained. We study the properties of the linear functional related to the new Stolarsky-type inequality, and finally apply these new results in the theory of fractional integrals.

  • [1]

    Abramovich, S. Pečarić, J., Varošanec, S. Further extension of Stolarsky’s inequality with general weights. Math. Pannon. 10 (1999), 249256.

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  • [2]

    Daraby, B. Investigation of a Stolarsky type inequality for integrals in pseudo-analysis. Fract. Calc. Appl. Anal., 13(5) (2010), 467473.

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  • [3]

    Katugampola, U. N. New approach to a generalized fractional integral. Appl. Math. Comput., 218 (2011), 860865.

  • [4]

    Maligranda, L., Pečarić, J., Persson, L. E. Stolarsky’s inequality with general weights. Proc. Amer. Math. Soc. 123(7) (1995), 21132117.

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  • [5]

    Pečarić, J. On Stolarsky’s quotient. Makedon. Akad. Nauk. Umet. Oddel. Mat.-Tehn. Nauk. 14(2) (1993), 5560.

  • [6]

    Pečarić, J. A reverse Stolarsky’s inequality. Amer. Math. Monthly, 101(6) (1994), 566568.

  • [7]

    Pečarić, J., Varošanec, S. Remarks on Gauss–Winckler’s and Stolarsky’s inequality. Utilitas Math. 48(1995), 233241.

  • [8]

    Pinelis, I. Multilinear direct and reverse Stolarsky inequalities. Math. Inequal. Appl. 5(4) (2002), 671691.

  • [9]

    Stolarsky, K. From Wythoff’s Nim to Chebyshev’s inequality. Amer. Math. Monthly, 98(10) (1991), 889900.

  • [10]

    Varošanec, S., Pečarić, J. Gauss’ and related inequalities. Z. Anal. Anwend. 14(1) (1995) 175183.

  • [11]

    Varošanec, S., Pečarić, J., Šunde, J. Some discrete inequalities. Z. Anal. Anwend. 15(4) (1996), 10251032.

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Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém, Hungary)
  • János PINTZ (Rényi Institute of Mathematics, Budapest, Hungary)
  • Ferenc SCHIPP (Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary)
  • Sándor SZABÓ (University of Pécs, Pécs, Hungary)

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz, Linz, Austria)
  • Ferenc HARTUNG (University of Pannonia, Veszprém, Hungary)
  • Ferenc WEISZ (Eötvös Loránd University, Budapest, Hungary)

Editorial Board

  • Attila BÉRCZES (University of Debrecen, Debrecen, Hungary)
  • István BERKES (Rényi Institute of Mathematics, Budapest, Hungary)
  • Károly BEZDEK (University of Calgary, Calgary, Canada)
  • György DÓSA (University of Pannonia, Veszprém, Hungary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs, Pécs, Hungary)
  • Vedran KRCADINAC (University of Zagreb, Zagreb, Croatia) 
  • Željka MILIN ŠIPUŠ (University of Zagreb, Zagreb, Croatia)
  • Gábor NYUL (University of Debrecen, Debrecen, Hungary)
  • Margit PAP (University of Pécs, Pécs, Hungary)
  • István PINK (University of Debrecen, Debrecen, Hungary)
  • Mihály PITUK (University of Pannonia, Veszprém, Hungary)
  • Lukas SPIEGELHOFER (Montanuniversität Leoben, Leoben, Austria)
  • Andrea ŠVOB (University of Rijeka, Rijeka, Croatia)
  • Csaba SZÁNTÓ (Babeş-Bolyai University, Cluj-Napoca, Romania)
  • Jörg THUSWALDNER (Montanuniversität Leoben, Leoben, Austria)
  • Zsolt TUZA (University of Pannonia, Veszprém, Hungary)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics, Budapest, Hungary)  - Chair
  • Gabriella BÖHM
  • György GÁT (University of Debrecen, Debrecen, Hungary)

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