A unified class of analytic functions associated with Erdeyi-Kober type integral operator

Document Type : Research Paper


School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, TN, India


Making use of the convolution product, we introduce a unified class of analytic functions with negative coefficients. Also, we obtain the coefficient bounds, extreme points and radius of starlikeness for functions belonging to the generalized class $ \mathcal{TP}_{\vartheta,\tau}^{a,c}(\alpha ,\beta).$  Furthermore, partial sums $f_k(z)$ of functions $f(z)$ in the class $\mathcal{P}_{\vartheta,\tau}^{a,c}(\alpha ,\beta)$ are considered and sharp lower bounds for the ratios of real part of $f(z)$ to $f_k(z)$ and $f'(z)$ to $f'_k(z)$ are determined. Relevant connections of the results with various known results are also considered.


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Volume 14, Issue 2
February 2023
Pages 385-397
  • Receive Date: 19 August 2021
  • Revise Date: 09 November 2021
  • Accept Date: 12 November 2021
  • First Publish Date: 15 June 2022