• Kyungpook Mathematical Journal
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• 제28권2호
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• pp.147-154
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• 1988

For a positive integer p, $A_p$ will denote the class of functions $f(z)=z^p+\sum\limits^{\infty}_{n=p+1}a_nz^n$ which are analytic in the unit disc U = {z: |z| <1}. For $0{\leq}{\alpha}{\leq}1$, 0<${\beta}{\leq}1$, $0{\leq}{\lambda}$ $S_p({\alpha},{\beta},{\lambda})$ denote the class of functions $f(z){\in}A_p$ which satisfy the condition $\left|\frac{{\frac{zf^{\prime}(z)}{f(z)}}-p}{{{\alpha}{\frac{zf^{\prime}(z)}{f(z)}}+p-{\lambda}(1+{\alpha})}}\right|$<${\beta}$ for $z{\in}U$ In this paper we obtain a representation theorem for the class $S_p({\alpha},{\beta},{\lambda})$ and also derive distortion theorem and sharp estimates for the coefficients of this class.

• 대한수학회보
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• 제52권6호
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• pp.1805-1818
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• 2015

In this article, we first consider a linear multiplier fractional q-differintegral operator and then use it to define new subclasses of p-valent analytic functions in the open unit disk U. An attempt has also been made to obtain two new q-integral operators and study their sufficient conditions on some classes of analytic functions. We also point out that the operators and classes presented here, being of general character, are easily reducible to yield many diverse new and known operators and function classes.

• 대한수학회보
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• 제43권1호
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• pp.179-188
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• 2006

For a given p-valent analytic function g with positive coefficients in the open unit disk $\Delta$, we study a class of functions $f(z) = z^p - \sum\limits{_{n=m}}{^\infty} a_nz^n(a_n{\geq}0)$ satisfying $$\frac 1 {p}{\Re}\;(\frac {z(f*g)'(z)} {(f*g)(z)})\;>\;\alpha\;(0{\leq}\;\alpha\;<\;1;z{\in}{\Delta})$$ Coefficient inequalities, distortion and covering theorems, as well as closure theorems are determined. The results obtained extend several known results as special cases.