<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

Publié en ligne: 02 déc. 2020

Pages: 294 - 306

Reçu: 29 avr. 2020

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

Mots clés
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

Publié en ligne: 02 déc. 2020

Pages: 294 - 306

Reçu: 29 avr. 2020

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

Mots clésanalytic 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.

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