Application of Fractional Calculus to a Class of Multivalent β -Uniformly Starlike Functions

J. J. Bhamare; S. M. Khairnar

doi:https://doi.org/10.14445/22315373/IJMTT-V12P517

International Journal of Mathematics Trends and Technology

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Volume 12 | Number 2 | Year 2014 | Article Id. IJMTT-V12P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V12P517

Application of Fractional Calculus to a Class of Multivalent β -Uniformly Starlike Functions

J. J. Bhamare, S. M. Khairnar

Abstract

In this paper we introduce a new class of multivalent functions which is β- uniformly starlike in the unit disc. Characterization property exhibited and relation with other fractional calculus operators are given. Connections with β-uniformly starlike and parabolic starlike functions are defined. Results on modified Hadamard product, extreme points, growth and distortion theorems, class preserving integral operators, region of p-valency and radius of β-uniformly starlike functions are also derived.

Keywords

β-uniformly starlike functions, Fractional calculus operator, Region of p-valency, Parabolic starlike functions, Incomplete beta functions..

References

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Citation :

J. J. Bhamare, S. M. Khairnar, "Application of Fractional Calculus to a Class of Multivalent β -Uniformly Starlike Functions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 12, no. 2, pp. 112-119, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V12P517