<abstract xmlns="http://www.w3.org/1999/xhtml">Let T<italic>n</italic> be the class of functions f which are defined by a power series
<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2020-0021_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><mi>z</mi><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><msub><mrow><mi>a</mi></mrow><mi>n</mi></msub><mn>2</mn><msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></msup><mo>+</mo><mo>…</mo></mrow></math><tex-math>f\left( z \right) = z + {a_{n + 1}}{z^{n + 1}} + {a_n}2{z^{n + 2}} + \ldots</tex-math></alternatives></disp-formula>
for every <italic>z</italic> in the closed unit disc <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2020-0021_eq_002.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>𝕌</mi><mo>¯</mo></mover></math><tex-math>\bar {\mathbb{U}}</tex-math></alternatives></inline-formula>. With m different boundary points <italic>z</italic>s, (s = 1,2,...,m), we consider α<italic>m</italic> ∈ <italic>e</italic>iβ𝒜−j−λf(𝕌), here 𝒜−j−λ is the generalized Alexander integral operator and 𝕌 is the open unit disc. Applying 𝒜−j−λ, a subclass B<italic>n</italic>(α<italic>m</italic>,β,ρ; j, λ) of T<italic>n</italic> is defined with fractional integral for functions f. The object of present paper is to consider some interesting properties of f to be in B<italic>n</italic>(α<italic>m</italic>,β,ρ; j, λ).</abstract>

Let Tn be the class of functions f which are defined by a power series
f(z)=z+an+1zn+1+an2zn+2+…f\left( z \right) = z + {a_{n + 1}}{z^{n + 1}} + {a_n}2{z^{n + 2}} + \ldots
for every z in the closed unit disc 𝕌¯\bar {\mathbb{U}}. With m different boundary points zs, (s = 1,2,...,m), we consider αm ∈ eiβ𝒜−j−λf(𝕌), here 𝒜−j−λ is the generalized Alexander integral operator and 𝕌 is the open unit disc. Applying 𝒜−j−λ, a subclass Bn(αm,β,ρ; j, λ) of Tn is defined with fractional integral for functions f. The object of present paper is to consider some interesting properties of f to be in Bn(αm,β,ρ; j, λ).

Generalized operator for Alexander integral operator

Faculty of Science, Department of Mathematics

Honorary Professor “1 Decembrie 1918” University Alba Iulia

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Generalized operator for Alexander integral operator"}

Let Tn be the class of functions f which are defined by a power series
f(z)=z+an+1zn+1+an2zn+2+…f\left( z \right) = z + {a_{n + 1}}{z^{n + 1}} + {a_n}2{z^{n +...

Generalized operator for Alexander integral operator

Published Online: Dec 02, 2020

Page range: 294 - 306

Received: Apr 29, 2020

DOI: https://doi.org/10.2478/ausm-2020-0021

Keywords
analytic function, Alexander integral operator, fractional integral, gamma function, Miller and Mocanu lemma

© 2020 H. Özlem Güney et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Generalized operator for Alexander integral operator

Published Online: Dec 02, 2020

Page range: 294 - 306

Received: Apr 29, 2020

DOI: https://doi.org/10.2478/ausm-2020-0021

Keywordsanalytic function, Alexander integral operator, fractional integral, gamma function, Miller and Mocanu lemma

© 2020 H. Özlem Güney et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
analytic function, Alexander integral operator, fractional integral, gamma function, Miller and Mocanu lemma