On Special Differential Subordinations Using Fractional Integral of Sălăgean and Ruscheweyh Operators

• Main Authors: Alina Alb Lupaş, Georgia Irina Oros
• Format: Article
• Language: English
• Published: MDPI AG 2021-08-01
• Series: Symmetry
• Subjects: differential subordination; convex function; best dominant; differential operator; fractional integral
• Online Access: https://www.mdpi.com/2073-8994/13/9/1553

In the present paper, a new operator denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>D</mi><mrow><mi>z</mi></mrow><mrow><mo>−</mo><mi>λ</mi></mrow></msubsup><msubsup><mi>L</mi><mrow><mi>α</mi></mrow><mi>n</mi></msubsup></mrow></semantics></math></inline-formula> is defined by using the fractional integral of Sălăgean and Ruscheweyh operators. By means of the newly obtained operator, the subclass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>S</mi><mi>n</mi></msub><mfenced separators="" open="(" close=")"><mi>δ</mi><mo>,</mo><mi>α</mi><mo>,</mo><mi>λ</mi></mfenced></mrow></semantics></math></inline-formula> of analytic functions in the unit disc is introduced, and various properties and characteristics of this class are derived by applying techniques specific to the differential subordination concept. By studying the operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>D</mi><mrow><mi>z</mi></mrow><mrow><mo>−</mo><mi>λ</mi></mrow></msubsup><msubsup><mi>L</mi><mrow><mi>α</mi></mrow><mi>n</mi></msubsup></mrow></semantics></math></inline-formula>, some interesting differential subordinations are also given.