A class of strongly close-to-convex functions

R. K. Raina; Poonam Sharma; Janusz Sokol

doi:10.5269/bspm.v38i6.38464

R. K. Raina M.P. University of Agriculture and Technology
Poonam Sharma University of Lucknow Department of Mathematics & Astronomy
Janusz Sokol University of Rzeszów Faculty of Mathematics and Natural Sciences

DOI: https://doi.org/10.5269/bspm.v38i6.38464

Abstract

In this paper, we study a class of strongly close-to-convex functions $f(z)$ analytic in the unit disk $\mathbb{U}$ with $f(0)=0,f^{\prime }(0)=1$ satisfying for some convex function $g(z)$ the condition that

\begin{equation*}

\frac{zf^{\prime }(z)}{g(z)}\prec \left( \frac{1+Az}{1+Bz}\right) ^{m}

\end{equation*}%

\begin{equation*}

\left( -1\leq A\leq 1,-1\leq B\leq 1\ \left( A\neq B\right) ,0<m\leq 1;z\in

\mathbb{U}\right) .

\end{equation*}%

We obtain for functions belonging to this class, the coefficient estimates, bounds, certain results based on an integral operator and radius of convexity. We also deduce a number of useful special cases and consequences of the various results which are presented in this paper.

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Author Biographies

R. K. Raina, M.P. University of Agriculture and Technology

Professor (Retd.) and Emeritus Fellow

Poonam Sharma, University of Lucknow Department of Mathematics & Astronomy

Department of Mathematics & Astronomy, Professor

Janusz Sokol, University of Rzeszów Faculty of Mathematics and Natural Sciences

Department of Mathematics , Professor

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