View More View Less
  • 1 Morsbacher Straße 10, 51545 Waldbröl, Germany
  • 2 The Hong Kong Polytechnic University, Hunghom, Hong Kong
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

Abstract

We prove: For all natural numbers n and real numbers x ∈ [0, π] we have 548130585k=1n(1)k+1(sin((2k1)x)2k1+sin(2kx)2k).

The sign of equality holds if and only if n = 2 and x = 4π/5.

  • [1]

    Alzer, H. and Koumandos, S., Sub- and superadditive properties of Fejér's sine polynomial, Bull. London Math. Soc., 38 (2006), 261268.

    • Search Google Scholar
    • Export Citation
  • [2]

    Alzer, H. and Kwong, M. K., On Young's inequality, J. Math. Anal. Appl., 469 (2019), 480492.

  • [3]

    Askey, R., Orthogonal Polynomials and Special Functions, Reg. Conf. Ser. Appl. Math. (vol. 21), SIAM, Philadelphia, PA, 1975.

  • [4]

    Askey, R. and Gasper, G., Inequalities for polynomials, in: The Bieberbach Conjecture (eds.: A. Baernstein II et al.), Mathematical Surveys and Monographs 21, Amer. Math. Soc., Providence, RI, 1986, 732.

    • Search Google Scholar
    • Export Citation
  • [5]

    Gasper, G., Positive sums of the classical orthogonal polynomials, SIAM J. Math. Anal., 8 (1977), 423447.

  • [6]

    Jackson, D., Über eine trigonometrische Summe, Rend. Circ. Mat. Palermo, 32 (1911), 257262.

  • [7]

    Knopp, K., Theorie und Anwendung der unendlichen Reihen, Springer, Berlin, 1964.

  • [8]

    Koumandos, S., Inequalities for trigonometric sums, in: Nonlinear Analysis (eds.: P. M. Pardalos et al.), Springer Optimization and its Applications, 68, New York, 2012, 387416.

    • Search Google Scholar
    • Export Citation
  • [9]

    Milovanović, G. V., Mitrinović, D. S. and Rassias, Th. M., Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Sci. Publ., Singapore, 1994.

    • Search Google Scholar
    • Export Citation
  • [10]

    Van Der Waerden, B. L., Algebra I, Springer, Berlin, 1971.

The author instruction is available in PDF.

Please, download the file from HERE

Manuscript submission: HERE

 

  • Impact Factor (2018): 0.309
  • Mathematics (miscellaneous) SJR Quartile Score (2018): Q3/li>
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21

Language: English, French, German

Founded in 1966
Publication: One volume of four issues annually
Publication Programme: 2020. Vol. 57.
Indexing and Abstracting Services:

  • CompuMath Citation Index
  • Mathematical Reviews
  • Referativnyi Zhurnal/li>
  • Research Alert
  • Science Citation Index Expanded (SciSearch)/li>
  • SCOPUS
  • The ISI Alerting Services

 

Subscribers can access the electronic version of every printed article.

Senior editors

Editor(s)-in-Chief: Pálfy Péter Pál

Managing Editor(s): Sági, Gábor

Editorial Board

  • Biró, András (Number theory)
  • Csáki, Endre (Probability theory and stochastic processes, Statistics)
  • Domokos, Mátyás (Algebra (Ring theory, Invariant theory))
  • Győri, Ervin (Graph and hypergraph theory, Extremal combinatorics, Designs and configurations)
  • O. H. Katona, Gyula (Combinatorics)
  • Márki, László (Algebra (Semigroup theory, Category theory, Ring theory))
  • Némethi, András (Algebraic geometry, Analytic spaces, Analysis on manifolds)
  • Pach, János (Combinatorics, Discrete and computational geometry)
  • Rásonyi, Miklós (Probability theory and stochastic processes, Financial mathematics)
  • Révész, Szilárd Gy. (Analysis (Approximation theory, Potential theory, Harmonic analysis, Functional analysis))
  • Ruzsa, Imre Z. (Number theory)
  • Soukup, Lajos (General topology, Set theory, Model theory, Algebraic logic, Measure and integration)
  • Stipsicz, András (Low dimensional topology and knot theory, Manifolds and cell complexes, Differential topology)
  • Szász, Domokos (Dynamical systems and ergodic theory, Mechanics of particles and systems)
  • Tóth, Géza (Combinatorial geometry)

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333
E-mail: smh.studia@renyi.mta.hu