On a Certain Subclass of Multivalent Function Defined by Generalized Ruscheweyh Derivative

Shivani Indora; Sushil Kumar Bissu; Manisha Summerwar

doi:doi:10.11648/j.pamj.20241306.14

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On a Certain Subclass of Multivalent Function Defined by Generalized Ruscheweyh Derivative

Shivani Indora^*, Sushil Kumar Bissu, Manisha Summerwar

Published in Pure and Applied Mathematics Journal (Volume 13, Issue 6)

Received: 3 November 2024 Accepted: 25 November 2024 Published: 18 December 2024

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Abstract

Fractional calculus is the prominent branch of applied mathematics, it deals with a lot of diverse possibility of finding differentiation as well as integration of function f(z) when the order of differentiation operator ‘D’ and integration operator ‘J’ is a real number or a complex number. The combination of fractional calculus with geometric function theory is the dynamic field of the current research scenario. It has many applications not only in the field of mathematics but also in the different fields like modern mathematical physics, electrochemistry, viscoelasticity, fluid dynamics, electromagnetic, the theory of partial differential equations systems, Mathematical modeling. Various new subclasses of univalent and multivalent functions defined by using different operators. In this research paper, we work on the formation of new subclass of analytic and multivalent functions defined under the open unit disk. By using Generalized Ruscheweyh derivative operator we define a new subclass of analytic and multivalent functions. The main aim of this research article is to derive interesting characteristics of new subclass of multivalent functions, which mainly include coefficient bound, growth and distortion bounds for function and its first derivative, extreme point and obtain unidirectional results for the multivalent functions which are belonging to this new subclass.

Published in	Pure and Applied Mathematics Journal (Volume 13, Issue 6)
DOI	10.11648/j.pamj.20241306.14
Page(s)	109-118
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

Fractional Derivative, Generalized Ruscheweyh Derivative, Multivalent Functions, Coefficient Bound

References

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APA Style

Indora, S., Bissu, S. K., Summerwar, M. (2024). On a Certain Subclass of Multivalent Function Defined by Generalized Ruscheweyh Derivative. Pure and Applied Mathematics Journal, 13(6), 109-118. https://doi.org/10.11648/j.pamj.20241306.14

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ACS Style

Indora, S.; Bissu, S. K.; Summerwar, M. On a Certain Subclass of Multivalent Function Defined by Generalized Ruscheweyh Derivative. Pure Appl. Math. J. 2024, 13(6), 109-118. doi: 10.11648/j.pamj.20241306.14

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AMA Style

Indora S, Bissu SK, Summerwar M. On a Certain Subclass of Multivalent Function Defined by Generalized Ruscheweyh Derivative. Pure Appl Math J. 2024;13(6):109-118. doi: 10.11648/j.pamj.20241306.14

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@article{10.11648/j.pamj.20241306.14,
  author = {Shivani Indora and Sushil Kumar Bissu and Manisha Summerwar},
  title = {On a Certain Subclass of Multivalent Function Defined by Generalized Ruscheweyh Derivative},
  journal = {Pure and Applied Mathematics Journal},
  volume = {13},
  number = {6},
  pages = {109-118},
  doi = {10.11648/j.pamj.20241306.14},
  url = {https://doi.org/10.11648/j.pamj.20241306.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20241306.14},
  abstract = {Fractional calculus is the prominent branch of applied mathematics, it deals with a lot of diverse possibility of finding differentiation as well as integration of function f(z) when the order of differentiation operator ‘D’ and integration operator ‘J’ is a real number or a complex number. The combination of fractional calculus with geometric function theory is the dynamic field of the current research scenario. It has many applications not only in the field of mathematics but also in the different fields like modern mathematical physics, electrochemistry, viscoelasticity, fluid dynamics, electromagnetic, the theory of partial differential equations systems, Mathematical modeling. Various new subclasses of univalent and multivalent functions defined by using different operators. In this research paper, we work on the formation of new subclass of analytic and multivalent functions defined under the open unit disk. By using Generalized Ruscheweyh derivative operator we define a new subclass of analytic and multivalent functions. The main aim of this research article is to derive interesting characteristics of new subclass of multivalent functions, which mainly include coefficient bound, growth and distortion bounds for function and its first derivative, extreme point and obtain unidirectional results for the multivalent functions which are belonging to this new subclass.},
 year = {2024}
}

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TY  - JOUR
T1  - On a Certain Subclass of Multivalent Function Defined by Generalized Ruscheweyh Derivative
AU  - Shivani Indora
AU  - Sushil Kumar Bissu
AU  - Manisha Summerwar
Y1  - 2024/12/18
PY  - 2024
N1  - https://doi.org/10.11648/j.pamj.20241306.14
DO  - 10.11648/j.pamj.20241306.14
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 109
EP  - 118
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20241306.14
AB  - Fractional calculus is the prominent branch of applied mathematics, it deals with a lot of diverse possibility of finding differentiation as well as integration of function f(z) when the order of differentiation operator ‘D’ and integration operator ‘J’ is a real number or a complex number. The combination of fractional calculus with geometric function theory is the dynamic field of the current research scenario. It has many applications not only in the field of mathematics but also in the different fields like modern mathematical physics, electrochemistry, viscoelasticity, fluid dynamics, electromagnetic, the theory of partial differential equations systems, Mathematical modeling. Various new subclasses of univalent and multivalent functions defined by using different operators. In this research paper, we work on the formation of new subclass of analytic and multivalent functions defined under the open unit disk. By using Generalized Ruscheweyh derivative operator we define a new subclass of analytic and multivalent functions. The main aim of this research article is to derive interesting characteristics of new subclass of multivalent functions, which mainly include coefficient bound, growth and distortion bounds for function and its first derivative, extreme point and obtain unidirectional results for the multivalent functions which are belonging to this new subclass.
VL  - 13
IS  - 6
ER  -

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Author Information

Shivani Indora

Department of Mathematics, Sophia Girls’ College (Autonomous), Ajmer, India

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Sushil Kumar Bissu

Department of Mathematics, Sophia Girls’ College (Autonomous), Ajmer, India; Department of Mathematics, Samrat Prithviraj Chauhan Government College, Ajmer, India

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Manisha Summerwar

Department of Mathematics, Sophia Girls’ College (Autonomous), Ajmer, India; Department of Mathematics, Government School, Nagure, India

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Plain Text BibTeX RIS

APA Style

Indora, S., Bissu, S. K., Summerwar, M. (2024). On a Certain Subclass of Multivalent Function Defined by Generalized Ruscheweyh Derivative. Pure and Applied Mathematics Journal, 13(6), 109-118. https://doi.org/10.11648/j.pamj.20241306.14

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ACS Style

Indora, S.; Bissu, S. K.; Summerwar, M. On a Certain Subclass of Multivalent Function Defined by Generalized Ruscheweyh Derivative. Pure Appl. Math. J. 2024, 13(6), 109-118. doi: 10.11648/j.pamj.20241306.14

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AMA Style

Indora S, Bissu SK, Summerwar M. On a Certain Subclass of Multivalent Function Defined by Generalized Ruscheweyh Derivative. Pure Appl Math J. 2024;13(6):109-118. doi: 10.11648/j.pamj.20241306.14

Copy | Download

@article{10.11648/j.pamj.20241306.14,
  author = {Shivani Indora and Sushil Kumar Bissu and Manisha Summerwar},
  title = {On a Certain Subclass of Multivalent Function Defined by Generalized Ruscheweyh Derivative},
  journal = {Pure and Applied Mathematics Journal},
  volume = {13},
  number = {6},
  pages = {109-118},
  doi = {10.11648/j.pamj.20241306.14},
  url = {https://doi.org/10.11648/j.pamj.20241306.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20241306.14},
  abstract = {Fractional calculus is the prominent branch of applied mathematics, it deals with a lot of diverse possibility of finding differentiation as well as integration of function f(z) when the order of differentiation operator ‘D’ and integration operator ‘J’ is a real number or a complex number. The combination of fractional calculus with geometric function theory is the dynamic field of the current research scenario. It has many applications not only in the field of mathematics but also in the different fields like modern mathematical physics, electrochemistry, viscoelasticity, fluid dynamics, electromagnetic, the theory of partial differential equations systems, Mathematical modeling. Various new subclasses of univalent and multivalent functions defined by using different operators. In this research paper, we work on the formation of new subclass of analytic and multivalent functions defined under the open unit disk. By using Generalized Ruscheweyh derivative operator we define a new subclass of analytic and multivalent functions. The main aim of this research article is to derive interesting characteristics of new subclass of multivalent functions, which mainly include coefficient bound, growth and distortion bounds for function and its first derivative, extreme point and obtain unidirectional results for the multivalent functions which are belonging to this new subclass.},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - On a Certain Subclass of Multivalent Function Defined by Generalized Ruscheweyh Derivative
AU  - Shivani Indora
AU  - Sushil Kumar Bissu
AU  - Manisha Summerwar
Y1  - 2024/12/18
PY  - 2024
N1  - https://doi.org/10.11648/j.pamj.20241306.14
DO  - 10.11648/j.pamj.20241306.14
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 109
EP  - 118
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20241306.14
AB  - Fractional calculus is the prominent branch of applied mathematics, it deals with a lot of diverse possibility of finding differentiation as well as integration of function f(z) when the order of differentiation operator ‘D’ and integration operator ‘J’ is a real number or a complex number. The combination of fractional calculus with geometric function theory is the dynamic field of the current research scenario. It has many applications not only in the field of mathematics but also in the different fields like modern mathematical physics, electrochemistry, viscoelasticity, fluid dynamics, electromagnetic, the theory of partial differential equations systems, Mathematical modeling. Various new subclasses of univalent and multivalent functions defined by using different operators. In this research paper, we work on the formation of new subclass of analytic and multivalent functions defined under the open unit disk. By using Generalized Ruscheweyh derivative operator we define a new subclass of analytic and multivalent functions. The main aim of this research article is to derive interesting characteristics of new subclass of multivalent functions, which mainly include coefficient bound, growth and distortion bounds for function and its first derivative, extreme point and obtain unidirectional results for the multivalent functions which are belonging to this new subclass.
VL  - 13
IS  - 6
ER  -

Copy | Download