A special comprehensive class of analytic functions defined by multiplier transformation

作者：Lupas Alina Alb^*

来源：Journal of Computational Analysis and Applications, 2010, 12(2): 387-395.

• differential subordination
• convex function
• best dominant
• differential operator

For functions belonging to the class S(m) (delta, alpha), delta is an element of [0, 1), alpha >= 0 kind m is an element of N, of normalized analytic functions in the open unit disc U, which are investigated in this paper, the author derives several interesting differential subordination results. These subordinations are established by means of a special case of the multiplier transformations I(p) (m, lambda, l) f (z) namely
I(p) (m, lambda, l) f(z) := z(p) + Sigma(infinity)(j=p+n) (p+lambda(j - 1) + l/p + l)(m) a(j)z(j),
where p, n is an element of N, m is an element of N boolean OR {0}, lambda, l >= 0 and f is an element of A(p, n),
A (p, n) = {f is an element of H(U) : f (z) = z(p) + Sigma(infinity)(j=p+n) a(j)z(j) , z is an element of U}.
A number of interesting consequences of some of these subordination results are discussed. Relevant connections of some of the new results obtained in this paper with those in earlier works are also provided.

• 出版日期2010-4