Certain subclasses of starlike functions of complex order involving the Hurwitz-Lerch Zeta function

G. Murugusundaramoorthy; K. Uma

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2010)

  • Volume: 54, Issue: 2
  • ISSN: 0365-1029

Abstract

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Making use of the Hurwitz-Lerch Zeta function, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients of complex order denoted by T S b μ ( α , β , γ ) and obtain coefficient estimates, extreme points, the radii of close to convexity, starlikeness and convexity and neighbourhood results for the class T S b μ ( α , β , γ ) . In particular, we obtain integral means inequalities for the function f ( z ) belongs to the class  T S b μ ( α , β , γ ) in the unit disc.

How to cite

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G. Murugusundaramoorthy, and K. Uma. "Certain subclasses of starlike functions of complex order involving the Hurwitz-Lerch Zeta function." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 54.2 (2010): null. <http://eudml.org/doc/289741>.

@article{G2010,
abstract = {Making use of the Hurwitz-Lerch Zeta function, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients of complex order denoted by $TS^\mu _b(\alpha , \beta , \gamma )$ and obtain coefficient estimates, extreme points, the radii of close to convexity, starlikeness and convexity and neighbourhood results for the class $TS^\mu _b(\alpha , \beta , \gamma )$. In particular, we obtain integral means inequalities for the function $f(z)$ belongs to the class $TS^\mu _b(\alpha , \beta , \gamma )$ in the unit disc.},
author = {G. Murugusundaramoorthy, K. Uma},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Univalent; starlike, convex; uniformly convex; uniformly starlike; Hadamard product; integral means; Hurwitz-Lerch Zeta function},
language = {eng},
number = {2},
pages = {null},
title = {Certain subclasses of starlike functions of complex order involving the Hurwitz-Lerch Zeta function},
url = {http://eudml.org/doc/289741},
volume = {54},
year = {2010},
}

TY - JOUR
AU - G. Murugusundaramoorthy
AU - K. Uma
TI - Certain subclasses of starlike functions of complex order involving the Hurwitz-Lerch Zeta function
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2010
VL - 54
IS - 2
SP - null
AB - Making use of the Hurwitz-Lerch Zeta function, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients of complex order denoted by $TS^\mu _b(\alpha , \beta , \gamma )$ and obtain coefficient estimates, extreme points, the radii of close to convexity, starlikeness and convexity and neighbourhood results for the class $TS^\mu _b(\alpha , \beta , \gamma )$. In particular, we obtain integral means inequalities for the function $f(z)$ belongs to the class $TS^\mu _b(\alpha , \beta , \gamma )$ in the unit disc.
LA - eng
KW - Univalent; starlike, convex; uniformly convex; uniformly starlike; Hadamard product; integral means; Hurwitz-Lerch Zeta function
UR - http://eudml.org/doc/289741
ER -

References

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