APPLIED SCIENCE & SCIENCE DOMAIN
Published October 20, 2022 | Version v1
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On a Certain Subclass of Analytic Functions using Carlson and Shaffer Operator

Authors/Creators

  • 1. Department of Mathematics, VSS University of Technology, Sidhi Vihar, Burla, Sambalpur-768017,India
  • 2. Department of Basic Science and Humanities, School of Engineering and Technology, GIET University, Gunupur, Rayagada-765022, India

Description

The main objective of the exploration is to solve Fekete-Szeg¨o problem and to find the sharp upper bound to the second Hankel determinant for a certain sub class J (a, c) of analytic functions created using Carlson-Shaffers operator in the unit disk. Coefficient bound of  is determined.

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References

  • C. Carathe'odory, Über den Variabilitatsbereich der Fourier'schen Konstanten von positiven harmonischen Funktionen, Rend. Circ. Mat. Palermo, 32(1911), 193-217.
  • B. C. Carlson and D.B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal., 15(4)(1984), 737-745.
  • P. L. Duren, Univalent Functions, Grundlehren der Mathematischen wissenschaften, 259, Springer-Verlag, New York, USA, 1983.
  • R. Ehrenborg, The Hankel determinant of exponential polynomials, Amer. Math. Monthly, 107(2000), 557-560.
  • M. Fekete and G. Szegö, Eine Bemerkung über ungerade schlichte Funktionen, J. Lond. Math. Soc., 8(1933), 85-89.
  • A. Janteng, S. A. Halim and M. Darus, Coefficient inequality for a function whose derivative has a positive real part, J. Inequal. Pure \& Appl. Math., 7(2)(2006), Art. 50.
  • A. Janteng, S.A. Halim and M. Darus, Estimate on the second Hankel functional for functions whose derivative has a positive real part, Journal of Quality Measurement and Analysis, 4(1)(2008), 189-195.
  • F. R. Keogh and E.P. Merkes, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., 20(1969), 8-12.
  • W. Koepf, On the Fekete-Szeg\"{o} problem for close-to-convex functions-II, Arch. Math. (Basel), 49(1987), 420-433.
  • W. Koepf, On the Fekete-Szeg\"{o} problem for close-to-convex functions, Proc. Amer. Math. Soc., 101(1)(1987), 89-95.