Starlike functions of complex order involving q-hypergeometric functions with fixed point

Kaliappan Vijaya; Gangadharan Murugusundaramoorthy; Murugesan Kasthuri

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2014)

  • Volume: 13, Issue: 1, page 51-63
  • ISSN: 2300-133X

Abstract

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Recently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with ƒ(ξ) = ƒ0(ξ) − 1 = 0, ξ (|ξ| = d) is a fixed point in the open disc U = {z ∈ ℂ: |z| < 1}. In this paper we define a new subclass of starlike functions of complex order based on q-hypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the function class T Sξ(α, β,γ). Further, we obtain integral means inequalities for the function ƒ ∈ T Sξ(α, β,γ).

How to cite

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Kaliappan Vijaya, Gangadharan Murugusundaramoorthy, and Murugesan Kasthuri. "Starlike functions of complex order involving q-hypergeometric functions with fixed point." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 13.1 (2014): 51-63. <http://eudml.org/doc/268762>.

@article{KaliappanVijaya2014,
abstract = {Recently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with ƒ(ξ) = ƒ0(ξ) − 1 = 0, ξ (|ξ| = d) is a fixed point in the open disc U = \{z ∈ ℂ: |z| < 1\}. In this paper we define a new subclass of starlike functions of complex order based on q-hypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the function class T Sξ(α, β,γ). Further, we obtain integral means inequalities for the function ƒ ∈ T Sξ(α, β,γ).},
author = {Kaliappan Vijaya, Gangadharan Murugusundaramoorthy, Murugesan Kasthuri},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {starlike functions, convex functions},
language = {eng},
number = {1},
pages = {51-63},
title = {Starlike functions of complex order involving q-hypergeometric functions with fixed point},
url = {http://eudml.org/doc/268762},
volume = {13},
year = {2014},
}

TY - JOUR
AU - Kaliappan Vijaya
AU - Gangadharan Murugusundaramoorthy
AU - Murugesan Kasthuri
TI - Starlike functions of complex order involving q-hypergeometric functions with fixed point
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2014
VL - 13
IS - 1
SP - 51
EP - 63
AB - Recently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with ƒ(ξ) = ƒ0(ξ) − 1 = 0, ξ (|ξ| = d) is a fixed point in the open disc U = {z ∈ ℂ: |z| < 1}. In this paper we define a new subclass of starlike functions of complex order based on q-hypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the function class T Sξ(α, β,γ). Further, we obtain integral means inequalities for the function ƒ ∈ T Sξ(α, β,γ).
LA - eng
KW - starlike functions, convex functions
UR - http://eudml.org/doc/268762
ER -

References

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