• Title/Summary/Keyword: subordinate and generalized fractional derivative

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CERTAIN CLASS OF FRACTIONAL CALCULUS OPERATOR WITH TWO FIXED POINTS

  • Kwon, Oh-Sang
    • East Asian mathematical journal
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    • v.14 no.1
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    • pp.107-116
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    • 1998
  • This paper deals with functions of the form $f(z)=a_1z-{\sum}{\limits}_{n=2}^{\infty}a_nz^n(a_1>0,\;a_n{\geqslant}0)$ with $(1-{\mu})f(z_0)/z_0+{\mu}f'(z_0)=1(-1. We introduce the class $\varphi({\mu},{\eta},{\gamma},{\delta},A,B;\;z_0)$ with generalized fractional derivatives. Also we have obtained coefficient inequalities, distortion theorem and radious problem of functions belonging to the calss $\varphi({\mu},{\eta},{\gamma},{\delta},A,B;\;z_0)$.

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