Some Properties of Multivalent Analytic Starlike Function Subordinated with Cosine Hyperbolic Function

Muhammad Azam; Naseer Ullah

doi:doi:10.11648/j.ijamtp.20210703.13

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Some Properties of Multivalent Analytic Starlike Function Subordinated with Cosine Hyperbolic Function

Muhammad Azam, Naseer Ullah

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 7, Issue 3)

Received: 2 June 2021 Accepted: 19 July 2021 Published: 11 September 2021

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Abstract

Abdullah Alotaibi defined a starlike function connected with a cosine hyperbolic function in the year 2020. We establish some appropriate conditions for several features of multivalent analytic starlike function subordinated with cosine hyperbolic function in this article. We determine conditions on α are subordinated by Janowski function. We acquire some suitable conditions by selecting specific values for functions we get some adequate conditions for multivalent starlik function related with cosine hyperbolic. Over the last decade, starlike functions have grown in popularity in both literature and application. Our goal in this work is look at some practical challenges with q-starlike functions. Moreover, we will show that the class described in this research, as well as the results gained, generalizes numerous previously published papers. We need to add some fundamental Geometric function theory literature here to comprehend the notions employed in our work in a straightforward way. To do so, we'll start with the notation, which signifies the class of holomorphic or analytic functions in the holomorphic or analytic functions. Then the relationships must be stable. In addition, all univalent functions will belong to the subfamily. Furthermore, the possibility of subjections between analytic functions and, as shown by, as; the functions, are related by the connection of subjection, if there exists an analytic function with restrictions and such that in addition, if the function is in, we get The aim of this paper is to define a family of multivalent q-starlike functions associated with circular domains and to study some of its useful properties of multivalent analytic functions subordinated cosine hyperbolic function.

Published in	International Journal of Applied Mathematics and Theoretical Physics (Volume 7, Issue 3)
DOI	10.11648/j.ijamtp.20210703.13
Page(s)	80-87
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Multivalent Functions, Janowski Function, Trigonometric Functions

References

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APA Style

Muhammad Azam, Naseer Ullah. (2021). Some Properties of Multivalent Analytic Starlike Function Subordinated with Cosine Hyperbolic Function. International Journal of Applied Mathematics and Theoretical Physics, 7(3), 80-87. https://doi.org/10.11648/j.ijamtp.20210703.13

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ACS Style

Muhammad Azam; Naseer Ullah. Some Properties of Multivalent Analytic Starlike Function Subordinated with Cosine Hyperbolic Function. Int. J. Appl. Math. Theor. Phys. 2021, 7(3), 80-87. doi: 10.11648/j.ijamtp.20210703.13

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AMA Style

Muhammad Azam, Naseer Ullah. Some Properties of Multivalent Analytic Starlike Function Subordinated with Cosine Hyperbolic Function. Int J Appl Math Theor Phys. 2021;7(3):80-87. doi: 10.11648/j.ijamtp.20210703.13

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@article{10.11648/j.ijamtp.20210703.13,
  author = {Muhammad Azam and Naseer Ullah},
  title = {Some Properties of Multivalent Analytic Starlike Function Subordinated with Cosine Hyperbolic Function},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {7},
  number = {3},
  pages = {80-87},
  doi = {10.11648/j.ijamtp.20210703.13},
  url = {https://doi.org/10.11648/j.ijamtp.20210703.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20210703.13},
  abstract = {Abdullah Alotaibi defined a starlike function connected with a cosine hyperbolic function in the year 2020. We establish some appropriate conditions for several features of multivalent analytic starlike function subordinated with cosine hyperbolic function in this article. We determine conditions on α are subordinated by Janowski function. We acquire some suitable conditions by selecting specific values for functions we get some adequate conditions for multivalent starlik function related with cosine hyperbolic. Over the last decade, starlike functions have grown in popularity in both literature and application. Our goal in this work is look at some practical challenges with q-starlike functions. Moreover, we will show that the class described in this research, as well as the results gained, generalizes numerous previously published papers. We need to add some fundamental Geometric function theory literature here to comprehend the notions employed in our work in a straightforward way. To do so, we'll start with the notation, which signifies the class of holomorphic or analytic functions in the holomorphic or analytic functions. Then the relationships must be stable. In addition, all univalent functions will belong to the subfamily. Furthermore, the possibility of subjections between analytic functions and, as shown by, as; the functions, are related by the connection of subjection, if there exists an analytic function with restrictions and such that in addition, if the function is in, we get The aim of this paper is to define a family of multivalent q-starlike functions associated with circular domains and to study some of its useful properties of multivalent analytic functions subordinated cosine hyperbolic function.},
 year = {2021}
}

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TY  - JOUR
T1  - Some Properties of Multivalent Analytic Starlike Function Subordinated with Cosine Hyperbolic Function
AU  - Muhammad Azam
AU  - Naseer Ullah
Y1  - 2021/09/11
PY  - 2021
N1  - https://doi.org/10.11648/j.ijamtp.20210703.13
DO  - 10.11648/j.ijamtp.20210703.13
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 80
EP  - 87
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20210703.13
AB  - Abdullah Alotaibi defined a starlike function connected with a cosine hyperbolic function in the year 2020. We establish some appropriate conditions for several features of multivalent analytic starlike function subordinated with cosine hyperbolic function in this article. We determine conditions on α are subordinated by Janowski function. We acquire some suitable conditions by selecting specific values for functions we get some adequate conditions for multivalent starlik function related with cosine hyperbolic. Over the last decade, starlike functions have grown in popularity in both literature and application. Our goal in this work is look at some practical challenges with q-starlike functions. Moreover, we will show that the class described in this research, as well as the results gained, generalizes numerous previously published papers. We need to add some fundamental Geometric function theory literature here to comprehend the notions employed in our work in a straightforward way. To do so, we'll start with the notation, which signifies the class of holomorphic or analytic functions in the holomorphic or analytic functions. Then the relationships must be stable. In addition, all univalent functions will belong to the subfamily. Furthermore, the possibility of subjections between analytic functions and, as shown by, as; the functions, are related by the connection of subjection, if there exists an analytic function with restrictions and such that in addition, if the function is in, we get The aim of this paper is to define a family of multivalent q-starlike functions associated with circular domains and to study some of its useful properties of multivalent analytic functions subordinated cosine hyperbolic function.
VL  - 7
IS  - 3
ER  -

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Author Information

Muhammad Azam

Faculty of Applied Science, School of Mathematics, Beijing University of Technology, Beijing, China
Naseer Ullah

Faculty of Applied Science, School of Mathematics, Beijing University of Technology, Beijing, China

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APA Style

Muhammad Azam, Naseer Ullah. (2021). Some Properties of Multivalent Analytic Starlike Function Subordinated with Cosine Hyperbolic Function. International Journal of Applied Mathematics and Theoretical Physics, 7(3), 80-87. https://doi.org/10.11648/j.ijamtp.20210703.13

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ACS Style

Muhammad Azam; Naseer Ullah. Some Properties of Multivalent Analytic Starlike Function Subordinated with Cosine Hyperbolic Function. Int. J. Appl. Math. Theor. Phys. 2021, 7(3), 80-87. doi: 10.11648/j.ijamtp.20210703.13

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AMA Style

Muhammad Azam, Naseer Ullah. Some Properties of Multivalent Analytic Starlike Function Subordinated with Cosine Hyperbolic Function. Int J Appl Math Theor Phys. 2021;7(3):80-87. doi: 10.11648/j.ijamtp.20210703.13

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@article{10.11648/j.ijamtp.20210703.13,
  author = {Muhammad Azam and Naseer Ullah},
  title = {Some Properties of Multivalent Analytic Starlike Function Subordinated with Cosine Hyperbolic Function},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {7},
  number = {3},
  pages = {80-87},
  doi = {10.11648/j.ijamtp.20210703.13},
  url = {https://doi.org/10.11648/j.ijamtp.20210703.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20210703.13},
  abstract = {Abdullah Alotaibi defined a starlike function connected with a cosine hyperbolic function in the year 2020. We establish some appropriate conditions for several features of multivalent analytic starlike function subordinated with cosine hyperbolic function in this article. We determine conditions on α are subordinated by Janowski function. We acquire some suitable conditions by selecting specific values for functions we get some adequate conditions for multivalent starlik function related with cosine hyperbolic. Over the last decade, starlike functions have grown in popularity in both literature and application. Our goal in this work is look at some practical challenges with q-starlike functions. Moreover, we will show that the class described in this research, as well as the results gained, generalizes numerous previously published papers. We need to add some fundamental Geometric function theory literature here to comprehend the notions employed in our work in a straightforward way. To do so, we'll start with the notation, which signifies the class of holomorphic or analytic functions in the holomorphic or analytic functions. Then the relationships must be stable. In addition, all univalent functions will belong to the subfamily. Furthermore, the possibility of subjections between analytic functions and, as shown by, as; the functions, are related by the connection of subjection, if there exists an analytic function with restrictions and such that in addition, if the function is in, we get The aim of this paper is to define a family of multivalent q-starlike functions associated with circular domains and to study some of its useful properties of multivalent analytic functions subordinated cosine hyperbolic function.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Some Properties of Multivalent Analytic Starlike Function Subordinated with Cosine Hyperbolic Function
AU  - Muhammad Azam
AU  - Naseer Ullah
Y1  - 2021/09/11
PY  - 2021
N1  - https://doi.org/10.11648/j.ijamtp.20210703.13
DO  - 10.11648/j.ijamtp.20210703.13
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 80
EP  - 87
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20210703.13
AB  - Abdullah Alotaibi defined a starlike function connected with a cosine hyperbolic function in the year 2020. We establish some appropriate conditions for several features of multivalent analytic starlike function subordinated with cosine hyperbolic function in this article. We determine conditions on α are subordinated by Janowski function. We acquire some suitable conditions by selecting specific values for functions we get some adequate conditions for multivalent starlik function related with cosine hyperbolic. Over the last decade, starlike functions have grown in popularity in both literature and application. Our goal in this work is look at some practical challenges with q-starlike functions. Moreover, we will show that the class described in this research, as well as the results gained, generalizes numerous previously published papers. We need to add some fundamental Geometric function theory literature here to comprehend the notions employed in our work in a straightforward way. To do so, we'll start with the notation, which signifies the class of holomorphic or analytic functions in the holomorphic or analytic functions. Then the relationships must be stable. In addition, all univalent functions will belong to the subfamily. Furthermore, the possibility of subjections between analytic functions and, as shown by, as; the functions, are related by the connection of subjection, if there exists an analytic function with restrictions and such that in addition, if the function is in, we get The aim of this paper is to define a family of multivalent q-starlike functions associated with circular domains and to study some of its useful properties of multivalent analytic functions subordinated cosine hyperbolic function.
VL  - 7
IS  - 3
ER  -

Copy | Download