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Differential subordinations for functions with positive real part using admissibility conditions

Meghna Sharma

Department of Mathematics, University of Delhi, Delhi 110 007, India

E-mail Address: meghnasharma203@gmail.com

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Sushil Kumar

Department of Applied Sciences, Bharati Vidyapeeth’s College of Engineering, Delhi 110063, India

E-mail Address: sushilkumar16n@gmail.com

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, and

Naveen Kumar Jain

https://orcid.org/0000-0003-0184-9965

Department of Mathematics, Aryabhatta College, Delhi 110021, India

E-mail Address: naveenjain05@gmail.com

Corresponding author.

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https://doi.org/10.1142/S1793557122500668Cited by:3 (Source: Crossref)

Abstract

Some sufficient conditions on certain constants which are involved in some first and second-order differential subordinations associated with certain functions with positive real part like modified Sigmoid function, exponential function and Janowski function are obtained so that the analytic function $p$ $p$ normalized by the condition $p (0) = 1$ $p (0) = 1$ , is subordinate to Janowski function. The admissibility conditions for Janowski function are used as a tool in the proof of the results. As application, several sufficient conditions are also computed for Janowski starlikeness.

Communicated by A. Escassut

Keywords:

AMSC: 30C45, 30C50

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