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Redheffer-Type Inequalities for the Fox–Wright Functions

  • Khaled MehrezEmail author
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

In this chapter, new sharpened Redheffer-type inequalities related to the Fox–Wright functions are established. As consequence, we show new Redheffer-type inequalities for hypergeometric functions and for the four-parametric Mittag-Leffler functions with best possible exponents.

Keywords

Fox–Wright function Sharpening Redheffer-type inequalities Hypergeometric function Four-parametric Mittag-Leffler function 

Mathematics Subject Classification (2010)

26D07 33C20 

References

  1. 1.
    R. Redheffer, Problem 5642. Am. Math. Mon. 76, 422 (1969)CrossRefGoogle Scholar
  2. 2.
    J.P. Williams, Solution of problem 5642. Am. Math. Mon. 76, 1153–1154 (1969)CrossRefGoogle Scholar
  3. 3.
    L. Zhu, J.J. Sun, Six new Redheffer-type inequalities for circular and hyperbolic functions. Comput. Math. Appl. 56, 522–529 (2008)MathSciNetCrossRefGoogle Scholar
  4. 4.
    L. Zhu, Extension of Redheffer type inequalities to modified Bessel functions. Appl. Math. Comput. 217, 8504–8506 (2011)MathSciNetzbMATHGoogle Scholar
  5. 5.
    K. Mehrez, Redheffer type inequalities for modified Bessel functions. Arab J. Math. Sci. 22(1), 38–42 (2016)MathSciNetzbMATHGoogle Scholar
  6. 6.
    K. Mehrez, Functional inequalities for the Wright functions. Integr. Trans. Spec. Functions 28(2), 130–144 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    A.M. Mathai, R.K. Saxena, The H-Function with Applications in Statistics and Other Disciplines (Wiley, New York, 1978)zbMATHGoogle Scholar
  8. 8.
    H.M. Srivastava, Z. Tomovski, Some problems and solutions involving Mathieu’s series and its generalization. J. Inequal. Pure Appl. Math. 5(2) Article 45, 1–3 (2004) (electronic)Google Scholar
  9. 9.
    R. Gorenflo, A.A. Kilbas, F. Mainardi, S.V. Rogosin, Mittag-Leffler Functions, Related Topics and Applications (Springer, Berlin, 2014)CrossRefGoogle Scholar
  10. 10.
    K. Mehrez, S.M. Sitnik, Functional Inequalities for the Mittag-Leffler Functions. Results Math. 72(1–2), 703–714 (2017)MathSciNetCrossRefGoogle Scholar
  11. 11.
    J. Paneva-Konovska, From Bessel to Multi-Index Mittag-Leffler Functions. Enumerable Families, Series in Them and Convergence (World Scientific, London, 2016)CrossRefGoogle Scholar
  12. 12.
    S. Ponnusamy, M. Vuorinen, Asymptotic expansions and inequalities for hypergeometric functions. Mathematika 44, 278–301 (1997)MathSciNetCrossRefGoogle Scholar
  13. 13.
    G.D. Anderson, M.K. Vamanamurthy, M. Vuorinen, Inequalities for quasiconformal mappings in space. Pac. J. Math. 160(1), 1–18 (1993)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Département de Mathématiques ISSAT KasserineUniversité de KairouanKairouanTunisia

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