Certain Properties of a Generalized Class of Analytic Functions Involving Some Convolution Operator

  • Faroze Ahmad Malik Department of Mathematics, Government Holkar (Model, Autonomous) Science College, Indore (M.P.)-452017, India
  • Nusrat Ahmed Dar Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India
  • Chitaranjan Sharma Department of Mathematics, Government Holkar (Model, Autonomous) Science College, Indore (M.P.)-452017, India
DOI: https://doi.org/10.34198/ejms.7121.4976
Keywords: convolution, uniform k-starlikeness (convexity), functions of complex order, integral means, subordination

Abstract

We use the concept of convolution to introduce and study the properties of a unified family 2021-05-28_21_54_19-Adobe_Acrobat_Professional_-_[EJMS070120214976.pdf]_1.png consisting of uniformly k-starlike and k-convex functions of complex order 2021-05-28_21_54_48-Adobe_Acrobat_Professional_-_[EJMS070120214976.pdf]_.png and type 2021-05-28_21_55_03-Adobe_Acrobat_Professional_-_[EJMS070120214976.pdf]_.png The family 2021-05-28_21_55_28-Adobe_Acrobat_Professional_-_[EJMS070120214976.pdf]_.png is a generalization of several other families of analytic functions available in literature. Apart from discussing the coefficient bounds, sharp radii estimates, extreme points and the subordination theorem for this family, we settle down the Silverman’s conjecture for integral means inequality. Moreover, invariance of this family under certain well-known integral operators is also established in this paper. Some previously known results are obtained as special cases.

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Published
2021-05-28
How to Cite
Malik, F. A., Dar, N. A., & Sharma, C. (2021). Certain Properties of a Generalized Class of Analytic Functions Involving Some Convolution Operator. Earthline Journal of Mathematical Sciences, 7(1), 49-76. https://doi.org/10.34198/ejms.7121.4976
Issue
Vol 7 No 1 (2021)
Section
Articles


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