Subordination Properties of Certain Operators Concerning Fractional Integral and Libera Integral Operator

Abstract

The results contained in this paper are the result of a study regarding fractional calculus combined with the classical theory of differential subordination established for analytic complex valued functions. A new operator is introduced by applying the Libera integral operator and fractional integral of order λ for analytic functions. Many subordination properties are obtained for this newly defined operator by using famous lemmas proved by important scientists concerned with geometric function theory, such as Eenigenburg, Hallenbeck, Miller, Mocanu, Nunokawa, Reade, Ruscheweyh and Suffridge. Results regarding strong starlikeness and convexity of order α are also discussed, and an example shows how the outcome of the research can be applied.

Keywords

• analytic function
• libera integral operator
• fractional integral of order <i>λ</i>
• differential subordination
• strongly of order <i>α</i>