Abstract
Let q1, q2 be univalent in Delta := {z : |z| < 1} and p be certain analytic function. We give some applications of first order differential subordinations and superordinations to obtain sufficient conditions to satisfy the following sandwich implication which is a generalization for various known sandwich theorems:
beta zq(1)(k)(z)q(1)(')(z) + Sigma(n)(j=0)alpha(j)q(1)(j) (z) < beta zp(k)(z) p'(z) + Sigma(n)(j=0)alpha(j)p(j)(z) < beta zp(2)(k)(z)q(2)'(z) + Sigma(n)(j=0)alpha(j)q(2)(j)(z)
implies q1(z) < p(z) < q2(z), where k is an element of Z and beta not equal 0, alpha(j)'(j)s is an element of C. Some of its special cases and its applications will be considered for certain analytic functions and certain linear operators.