<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this note, an extensive result consisting of several relations between certain inequalities and normalized analytic functions is first stated and some consequences of the result together with some examples are next presented. For the proof of the presented result, some of the assertions indicated in <xref ref-type="bibr" rid="j_ausm-2018-0028_ref_005_w2aab3b7c11b1b6b1ab1ab5Aa">[5]</xref>, <xref ref-type="bibr" rid="j_ausm-2018-0028_ref_008_w2aab3b7c11b1b6b1ab1ab8Aa">[8]</xref> and <xref ref-type="bibr" rid="j_ausm-2018-0028_ref_011_w2aab3b7c11b1b6b1ab1ac11Aa">[11]</xref> along with the results in <xref ref-type="bibr" rid="j_ausm-2018-0028_ref_003_w2aab3b7c11b1b6b1ab1ab3Aa">[3]</xref> and <xref ref-type="bibr" rid="j_ausm-2018-0028_ref_004_w2aab3b7c11b1b6b1ab1ab4Aa">[4]</xref> are also considered.</p></abstract>

In this note, an extensive result consisting of several relations between certain inequalities and normalized analytic functions is first stated and some consequences of the result together with some examples are next presented. For the proof of the presented result, some of the assertions indicated in [5], [8] and [11] along with the results in [3] and [4] are also considered.

A note on some relations between certain inequalities and normalized analytic functions

Department of Mathematics, Faculty of Science

Acta Universitatis Sapientiae, Mathematica

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

In this note, an extensive result consisting of several relations between certain inequalities and normalized analytic functions is first stated and some...

A note on some relations between certain inequalities and normalized analytic functions

Published Online: Mar 04, 2019

Page range: 368 - 374

Received: Jun 11, 2017

DOI: https://doi.org/10.2478/ausm-2018-0028

Keywords
complex plane, domains in the complex plane, differential inequalities in the complex plane, normalized analytic functions, univalent, starlikeness, convexity

© 2018 Müfit Şan et al., published by Sciendo

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

A note on some relations between certain inequalities and normalized analytic functions

Published Online: Mar 04, 2019

Page range: 368 - 374

Received: Jun 11, 2017

DOI: https://doi.org/10.2478/ausm-2018-0028

Keywordscomplex plane, domains in the complex plane, differential inequalities in the complex plane, normalized analytic functions, univalent, starlikeness, convexity

© 2018 Müfit Şan et al., published by Sciendo

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

Keywords
complex plane, domains in the complex plane, differential inequalities in the complex plane, normalized analytic functions, univalent, starlikeness, convexity