Convolution Properties of a Class of Analytic Functions

  • Khalida Inayat Noor COMSATS University Islamabad, Park Road, Tarlai Kalan, Islamabad 45550, Pakistan
  • Afis Saliu Department of Mathematics, University of the Gambia, MDI Road, Kanifing, P.O. Box 3530, Serrekunda, The Gambia
Keywords: convolution, subordination, starlike functions, conic domains, Janowski functions, Libera operator


In this paper, we introduce a new class $\mathcal{R}^{\alpha}_{m}(h)$ of functions $F=f\ast\psi$, defined in the open unit disc $E$ with $F(0)=F^{\prime}(0)-1=0$ and satisfying the condition
F^{\prime}(z)+\alpha zF^{\prime\prime}(z)=\left(\frac{m}{4}+\frac{1}{2}\right)p_{_{1}}(z)-\left(\frac{m}{4}-\frac{1}{2}\right)p_{_{2}}(z),
for $\alpha\geq0,\,m\geq2$ and $p_{_{i}}\prec h,\, i=1,2.$

Several convolution properties of this class are obtained by using the method of differential subordination. Many relevant connections of the findings here with those in earlier works are pointed out as special cases.


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How to Cite
Noor, K. I., & Saliu, A. (2023). Convolution Properties of a Class of Analytic Functions. Earthline Journal of Mathematical Sciences, 12(1), 109-120.