Third-Order Differential Subordination Features of Meromorphic Functions: Erdelyi–Kober Model Integral Operator Application

This study is concerned with the class of p-valent meromorphic functions, represented by the series <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mrow><mo>(</mo>&...

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Bibliographic Details
Main Authors: Ibrahim S. Elshazly, Borhen Halouani, Rabha M. El-Ashwah, Alaa H. El-Qadeem, Gangadharan Murugusundaramoorthy
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Axioms
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Online Access:https://www.mdpi.com/2075-1680/13/11/770
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Summary:This study is concerned with the class of p-valent meromorphic functions, represented by the series <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mrow><mo>(</mo><mi>ζ</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>ζ</mi><mrow><mo>−</mo><mi>p</mi></mrow></msup><mo>+</mo><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn><mo>−</mo><mi>p</mi></mrow><mo>∞</mo></msubsup><msub><mi>d</mi><mi>k</mi></msub><msup><mi>ζ</mi><mi>k</mi></msup></mrow></semantics></math></inline-formula>, with the domain characterized by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mo>|</mo><mi>ζ</mi><mo>|</mo><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>. We apply an Erdelyi–Kober-type integral operator to derive two recurrence relations. From this, we draw specific conclusions on differential subordination and differential superordination. By looking into suitable classes of permitted functions, we obtain various outcomes, including results analogous to sandwich-type theorems. The operator used can provide generalizations of previous operators through specific parameter choices, thus providing more corollaries.
ISSN:2075-1680