Differential subordinations involving arithmetic and geometric means

作者：Crisan O; Kanas S^*

来源：Applied Mathematics and Computation, 2013, 222: 123-131.

DOI：10.1016/j.amc.2013.07.051

• Univalent functions
• Subordination
• Differential subordination
• Arithmetic means
• Geometric means

The paper concerns the differential subordination with the expression combined by arithmetic and geometric means:
alpha[p(z)](delta) + (1 - alpha) [p(z) + zp'(z)/p(z)](mu) < phi(z), (p(0) = phi(0) = 1, vertical bar z vertical bar < 1),
where delta, mu and alpha are real numbers such that delta, mu is an element of < 1, 2 >, alpha is an element of < 0, 1 >. For delta is an element of < 1, 2 >, mu is an element of < 0, 1 >, alpha is an element of < 0, 1 > we also study the differential subordination
alpha[p(z)](delta) + (1 - alpha)[p(z)](mu) [p(z) + zp'(z)/p(z)](1-mu) < phi(z), (p(0) = phi(0) = 1, vertical bar z vertical bar < 1).
Several applications of the studied subordination in the theory of analytic functions are given.

• 出版日期2013-10-1