Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MONOTONICITY PROPERTIES OF THE BESSEL-STRUVE KERNEL

  • Baricz, Arpad (Institute of Applied Mathematics Obuda University) ;
  • Mondal, Saiful R. (Department of Mathematics and Statistics King Faisal University) ;
  • Swaminathan, Anbhu (Department of Mathematics Indian Institute of Technology Roorkee)
  • Received : 2015.12.12
  • Published : 2016.11.30
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Abstract

In this paper our aim is to study the classical Bessel-Struve kernel. Monotonicity and log-convexity properties for the Bessel-Struve kernel, and the ratio of the Bessel-Struve kernel and the Kummer confluent hypergeometric function are investigated. Moreover, lower and upper bounds are given for the Bessel-Struve kernel in terms of the exponential function and some $Tur{\acute{a}}n$ type inequalities are deduced.

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References

  1. A. Baricz, Bounds for modified Bessel functions of the first and second kinds, Proc. Edinb. Math. Soc. (2) 53 (2010), no. 3, 575-599. https://doi.org/10.1017/S0013091508001016
  2. A. Baricz and T. K. Pogany, Functional inequalities for modified Struve functions, Proc. Roy. Soc. Edinburgh Sect. A 144 (2014), no. 5, 891-904. https://doi.org/10.1017/S0308210512001370
  3. M. Biernacki and J. Krzyz, On the monotonity of certain functionals in the theory of analytic functions, Ann. Univ. Mariae Curie-Sk lodowska. Sect. A. 9 (1955), 135-147.
  4. A. Gasmi and M. Sifi, The Bessel-Struve intertwining operator on C and mean-periodic functions, Int. J. Math. Math. Sci. (2004), no. 57-60, 3171-3185.
  5. A. Gasmi and F. Soltani, Fock spaces for the Bessel-Struve kernel, J. Anal. Appl. 3 (2005), no. 2, 91-106.
  6. L. Kamoun and M. Sifi, Bessel-Struve intertwining operator and generalized Taylor series on the real line, Integral Transforms Spec. Funct. 16 (2005), no. 1, 39-55. https://doi.org/10.1080/1065246042000272063
  7. D. Karp and S. M. Sitnik, Log-convexity and log-concavity of hypergeometric-like functions, J. Math. Anal. Appl. 364 (2010), no. 2, 384-394. https://doi.org/10.1016/j.jmaa.2009.10.057
  8. D. S. Mitrinovic, Analytic Inequalities, Springer, New York, 1970.