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- W2607095604 abstract "For any real number ${itbeta}$ with ${itbeta}>1$ , let ${mathcal{M}}(,{itbeta})$ ( ${mathcal{N}}(,{itbeta})$ respectively) denote the class of analytic functions $f$ in the unit disk $mathbb{D}:={zin mathbb{C}:|z|<1}$ of the form $f(z)=z+sum _{n=2}^{infty }a_{n}z^{n}$ and satisfying $text{Re},P_{f}<{itbeta}$ ( $text{Re},Q_{f}<{itbeta}$ respectively) in $mathbb{D}$ , where $P_{f}=zf^{prime }(z)/f(z)$ and $Q_{f}=1+zf^{prime prime }(z)/f^{prime }(z)$ . Also, for ${itbeta}>1$ , let ${mathcal{M}}{rmSigma}(,{itbeta})$ ( ${mathcal{N}}{rmSigma}(,{itbeta})$ respectively) denote the class of analytic functions $g$ of the form $g(z)=z(1+sum _{n=1}^{infty }b_{n}z^{-n})$ and satisfying $text{Re},P_{g}<{itbeta}$ ( $text{Re},Q_{g}<{itbeta}$ respectively) for $zin {rmDelta}={zin mathbb{C}:1<|z|<infty }$ . In this paper, we shall determine the coefficient bounds, inverse coefficient bounds, the growth and distortion theorem and the upper bounds for the Fekete–Szegő functional ${rmLambda}_{{itlambda}}(f)=a_{3}-{itlambda}a_{2}^{2}$ for functions $f$ in the classes ${mathcal{M}}(,{itbeta})$ and ${mathcal{N}}(,{itbeta})$ . Further, we shall solve the maximal area problem for functions of the type $z/f(z)$ when $fin {mathcal{M}}(,{itbeta})$ , which is Yamashita’s conjecture for the class ${mathcal{M}}(,{itbeta})$ . We shall obtain the radius of convexity for the class ${mathcal{N}}(,{itbeta})$ . We shall also determine the coefficient bounds for functions $g$ in the classes ${mathcal{M}}{rmSigma}(,{itbeta})$ and ${mathcal{N}}{rmSigma}(,{itbeta})$ and the inverse coefficient bounds for functions $g$ in the class ${mathcal{M}}{rmSigma}(,{itbeta})$ . All the results are sharp." @default.
- W2607095604 created "2017-04-28" @default.
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- W2607095604 date "2015-09-29" @default.
- W2607095604 modified "2023-10-01" @default.
- W2607095604 title "COEFFICIENT INEQUALITIES AND YAMASHITA’S CONJECTURE FOR SOME CLASSES OF ANALYTIC FUNCTIONS" @default.
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- W2607095604 doi "https://doi.org/10.1017/s1446788715000336" @default.
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