<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

Publié en ligne: 27 févr. 2020

Pages: 430 - 436

Reçu: 21 mai 2019

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

Mots clés
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

Publié en ligne: 27 févr. 2020

Pages: 430 - 436

Reçu: 21 mai 2019

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

Mots clésanalytic 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.

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