Initial Coefficient Estimates and Fekete–Szegö Inequalities for New Families of Bi-Univalent Functions Governed by (<i>p</i> − <i>q</i>)-Wanas Operator
The motivation of the present article is to define the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mi>q</mi><mo>)<...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | article |
| Language: | EN |
| Published: |
MDPI AG
2021
|
| Subjects: | |
| Online Access: | https://doaj.org/article/c8b9e22eaab54606b13f3854a6e8d56c |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | The motivation of the present article is to define the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Wanas operator in geometric function theory by the symmetric nature of quantum calculus. We also initiate and explore certain new families of holormorphic and bi-univalent functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">A</mi><mi>E</mi></msub><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>σ</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>;</mo><mi>ϑ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>S</mi><mi>E</mi></msub><mrow><mo>(</mo><mi>μ</mi><mo>,</mo><mi>γ</mi><mo>,</mo><mi>σ</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>;</mo><mi>ϑ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> which are defined in the unit disk <i>U</i> associated with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Wanas operator. The upper bounds for the initial Taylor–Maclaurin coefficients and Fekete–Szegö-type inequalities for the functions in these families are obtained. Furthermore, several consequences of our results are pointed out based on the various special choices of the involved parameters. |
|---|