<abstract xmlns="http://www.w3.org/1999/xhtml">

Let 𝒜 <italic>p </italic>be the class of functions <italic>f</italic> of the form <disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_awutm-2022-0004_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>z</mi></mrow><mi>p</mi></msup><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>p</mi><mo>+</mo><mn>1</mn></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>p</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>p</mi><mo>+</mo><mn>2</mn></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>p</mi><mo>+</mo><mn>2</mn></mrow></msup><mo>+</mo><mo>⋯</mo></mrow></math>
<tex-math>f\left( z \right) = {z^p} + {a_{p + 1}}{z^{p + 1}} + {a_{p + 2}}{z^{p + 2}} + \cdots</tex-math>
</alternatives>
</disp-formula> that are analytic in the open unit disk 𝕌. For <italic>f</italic> ∈ 𝒜 <italic>p</italic>, new integral and differential operator <italic>nf</italic> is considered. The object of the present paper is to discuss some interesting properties of <italic>nf</italic> and to consider some examples for our results.
</abstract>

Let 𝒜 p be the class of functions f of the form 


f(z)=zp+ap+1zp+1+ap+2zp+2+⋯
f\left( z \right) = {z^p} + {a_{p + 1}}{z^{p + 1}} + {a_{p + 2}}{z^{p + 2}} +  \cdots

 that are analytic in the open unit disk 𝕌. For f ∈ 𝒜 p, new integral and differential operator nf is considered. The object of the present paper is to discuss some interesting properties of nf and to consider some examples for our results.

Generalizations of Libera integral operator for analytic functions

Department of Mathematics and Computer Science, Faculty of Science and Letters

Department of Mathematics, Faculty of Science

Honorary Professor of “1 Decembrie 1918” University of Alba Iulia

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Generalizations of Libera integral operator for analytic functions"}

Let 𝒜 p be the class of functions f of the form 


f(z)=zp+ap+1zp+1+ap+2zp+2+⋯
f\left( z \right) = {z^p} + {a_{p + 1}}{z^{p + 1}} + {a_{p + 2}}{z^{p + 2}} + ...

Generalizations of Libera integral operator for analytic functions

Published Online: Jun 20, 2022

Page range: 39 - 55

DOI: https://doi.org/10.2478/awutm-2022-0004

Keywords
Libera integral operator, -valently starlike function, -valently convex function, convolution, subordination

© 2022 Emel Yavuz et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Generalizations of Libera integral operator for analytic functions

Published Online: Jun 20, 2022

Page range: 39 - 55

DOI: https://doi.org/10.2478/awutm-2022-0004

KeywordsLibera integral operator, -valently starlike function, -valently convex function, convolution, subordination

© 2022 Emel Yavuz et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Libera integral operator, -valently starlike function, -valently convex function, convolution, subordination