<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we define a class of analytic functions, ℱ(ℋ, α, δ, µ), satisfying the following condition<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2019-0031_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>(</mo><mrow><mi>α</mi><msup><mrow><mrow><mrow><mo>[</mo><mrow><mfrac><mrow><mtext>z</mtext><mtext>f</mtext><msup><mo>′</mo></msup><mo>(</mo><mtext>z</mtext><mo>)</mo></mrow><mrow><mtext>f</mtext><mo>(</mo><mtext>z</mtext><mo>)</mo></mrow></mfrac></mrow><mo>]</mo></mrow></mrow></mrow><mi>δ</mi></msup><mo>+</mo><mo>(</mo><mn>1</mn><mo>-</mo><mi>α</mi><mo>)</mo><msup><mrow><mrow><mrow><mo>[</mo><mrow><mfrac><mrow><mtext>z</mtext><mtext>f</mtext><msup><mo>′</mo></msup><mrow><mo>(</mo><mtext>z</mtext><mo>)</mo></mrow></mrow><mrow><mtext>f</mtext><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mfrac></mrow><mo>]</mo></mrow></mrow></mrow><mi>μ</mi></msup><msup><mrow><mrow><mrow><mo>[</mo><mrow><mn>1</mn><mo>+</mo><mfrac><mrow><mtext>z</mtext><mtext>f</mtext><mo>″</mo><mo>(</mo><mtext>z</mtext><mo>)</mo></mrow><mrow><mtext>f</mtext><msup><mo>′</mo></msup><mo>(</mo><mtext>z</mtext><mo>)</mo></mrow></mfrac></mrow><mo>]</mo></mrow></mrow></mrow><mrow><mn>1</mn><mo>-</mo><mi>μ</mi></mrow></msup></mrow><mo>)</mo></mrow><mo>≺</mo><mo>𝒣</mo><mo>(</mo><mtext>z</mtext><mo>,</mo><mtext>t</mtext><mo>)</mo><mo>,</mo></mrow></math><tex-math>\left( {\alpha {{\left[ {{{{\rm{zf'}}({\rm{z}})} \over {{\rm{f}}(z)}}} \right]}^\delta } + (1 - \alpha ){{\left[ {{{{\rm{zf'}}\left( {\rm{z}} \right)} \over {{\rm{f}}(z)}}} \right]}^\mu }{{\left[ {1 + {{{\rm{zf''}}({\rm{z}})} \over {{\rm{f'}}({\rm{z}})}}} \right]}^{1 - \mu }}} \right)\,\, \prec \mathcal{H}({\rm{z}},{\rm{t}}),</tex-math></alternatives></disp-formula>where α ∈ [0, 1], δ ∈ [1, 2] and µ ∈ [0, 1].We give coefficient estimates and Fekete-Szegö inequality for this class.</abstract>

In this paper, we define a class of analytic functions, ℱ(ℋ, α, δ, µ), satisfying the following condition(α[zf′(z)f(z)]δ+(1-α)[zf′(z)f(z)]μ[1+zf″(z)f′(z)]1-μ)≺𝒣(z,t),\left( {\alpha {{\left[ {{{{\rm{zf'}}({\rm{z}})} \over {{\rm{f}}(z)}}} \right]}^\delta } + (1 - \alpha ){{\left[ {{{{\rm{zf'}}\left( {\rm{z}} \right)} \over {{\rm{f}}(z)}}} \right]}^\mu }{{\left[ {1 + {{{\rm{zf''}}({\rm{z}})} \over {{\rm{f'}}({\rm{z}})}}} \right]}^{1 - \mu }}} \right)\,\, \prec \mathcal{H}({\rm{z}},{\rm{t}}),where α ∈ [0, 1], δ ∈ [1, 2] and µ ∈ [0, 1].We give coefficient estimates and Fekete-Szegö inequality for this class.

Coefficient estimates and Fekete-Szegö inequality for a class of analytic functions satisfying subordinate condition associated with Chebyshev polynomials

Department of Mathematics, Faculty of Mathematics and Computer Science

Department of Mathematics, Faculty of Arts and Science

Acta Universitatis Sapientiae, Mathematica

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

In this paper, we define a class of analytic functions, ℱ(ℋ, α, δ, µ), satisfying the following...

Coefficient estimates and Fekete-Szegö inequality for a class of analytic functions satisfying subordinate condition associated with Chebyshev polynomials

Published Online: Feb 27, 2020

Page range: 430 - 436

Received: May 21, 2019

DOI: https://doi.org/10.2478/ausm-2019-0031

Keywords
analytic functions, subordination, Chebyshev polynomials, coefficient estimates, Fekete-Szegö inequality

© 2019 Eszter Szatmari et al., published by Sciendo

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

Coefficient estimates and Fekete-Szegö inequality for a class of analytic functions satisfying subordinate condition associated with Chebyshev polynomials

Published Online: Feb 27, 2020

Page range: 430 - 436

Received: May 21, 2019

DOI: https://doi.org/10.2478/ausm-2019-0031

Keywordsanalytic functions, subordination, Chebyshev polynomials, coefficient estimates, Fekete-Szegö inequality

© 2019 Eszter Szatmari et al., published by Sciendo

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

Keywords
analytic functions, subordination, Chebyshev polynomials, coefficient estimates, Fekete-Szegö inequality