On Certain Subclasses of Starlike p-valent Functions
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The object of the present paper is toinvestigate the starlikeness of the class of functions $f(z)=z^{p}+\sum%\limits_{k=n}^{\infty }a_{p+k}z^{p+k}\ (p,n\in \mathbb{N} =\left\{ 1,2,...\right\} )\ $which are analytic and $p-$valent in the unitdisc $U$ and satisfy the condition\begin{equation*}\left\vert (1-\lambda )(\frac{f(z)}{z^{p}})^{\alpha }+\lambda \frac{%zf^{^{\prime }}(z)}{pf(z)}(\frac{f(z)}{z^{p}})^{\alpha }-1\right\vert <\mu \\ \left( 0<\mu \leq 1,\lambda \geq 0,\alpha >0,z\in U\right) . \end{equation*} The starlikeness of certain integral operator are also discussed. Theresults obtained generalize the related works of some authors and some othernew results are also obtained.
Abstract
The object of the present paper is toinvestigate the starlikeness of the class of functions $f(z)=z^{p}+\sum%\limits_{k=n}^{\infty }a_{p+k}z^{p+k}\ (p,n\in \mathbb{N} =\left\{ 1,2,...\right\} )\ $which are analytic and $p-$valent in the unitdisc $U$ and satisfy the condition\begin{equation*}\left\vert (1-\lambda )(\frac{f(z)}{z^{p}})^{\alpha }+\lambda \frac{%zf^{^{\prime }}(z)}{pf(z)}(\frac{f(z)}{z^{p}})^{\alpha }-1\right\vert <\mu \\ \left( 0<\mu \leq 1,\lambda \geq 0,\alpha >0,z\in U\right) . \end{equation*} The starlikeness of certain integral operator are also discussed. Theresults obtained generalize the related works of some authors and some othernew results are also obtained.
참고문헌 (20)
- M. K. Aouf, "Certain admissible classes of mul-tivalent functions", J. Complex Anal., 2014 (2014)
- H. Daghreery, "Properties of some subclasses of analytic functions", 석사, pp.2009
- H. E. Darwish, "Certain subclass of meromorphicp- valent functions with alternating coefficients", J. Basic. Appl. Sci., 13(2), pp.108~119 (2013)
- H. E. Darwish, "On a certain subclass of analytic functions defined by a generalized differential operator and multiplier transformation", J. Frac. Cal. Appl., 5(2), pp.16~27 (2014)
- S. S. Miller, "Differential Subordinations and univalent functions", Michigan Math. J., 28(2), pp.157~171 (1981)
- M. Nunokawa, "An improvement of Ozaki's condition", Appl. Math. Com-put., 219(22), pp.10768~10776 (2013)
- M. Nunokawa, "Remarks on some starlike functions", J. Ineq. Appl., 2013 (2013)
- S. Ponnusamy, "Polya-Schoenberg conjecture by Caratheodory functions", J. London Math. Soc., 51(2), pp.93~104 (1995)
- S. Ponnusamy, "New sufficient conditions for starlike and univalent functions", Soochow J. Math., 21(2), pp.193~201 (1995)
- S. Ponnusamy, "Convolution properties of some classes of analytic functions", J. Math. Sci., 89(1), pp.1009~1020 (1998)
- S. Siregar, "The starlikeness of analytic functions of Koebe type", Math. Comput. Model., 54(11-12), pp.2928~2938 (2011)
- S. Sivasubramanian, "On the starlikeness of certain class of analytic functions", Math. Comput. Model., 54(1-2), pp.112~118 (2011)
- J. Soko, "A family of convolution operators for multivalent analytic functions", European J. Pure. Appl. Math., 5(4), pp.469~479 (2012)
- J. Soko l, "On some sufficient conditions for univalence and star-likeness", J. Ineq. Appl., 2012 (2012)
- H. M. Srivastava, "Subordination properties of certain classes of multivalently analytic functions", Math. Comput. Model., 52(3-4), pp.596~602 (2010)
- H. M. Srivastava, "A certain subclass of multivalent functions involving higher-order derivatives", Filomat, 30(1), pp.113~124 (2016)
- Z. -G. Wang, "Some criteria for meromorphic multivalent starlike functions", Appl. Math. Comput., 218(3), pp.1107~1111 (2011)
- Z. -G. Wang, "Some basic properties of certain subclasses of meromorphically starlike functions", J. Ineq. Appl., 2014 (2014)
- Z. -G. Wang, "Some properties of certain meromorphic close-to-convex functions", Appl. Math. Letters., 25(3), pp.454~460 (2012)
- D. Yang, "Some multivalent starlikeness conditions for analytic functions", Bull. Inst. Math. Acad. Sinica., 33(1), pp.55~67 (2005)