On a Subclass of P-Valent Functions Defined by a Generalized Salagean Operator

Ozokeraha Christiana Funmilayo

doi:doi:10.11648/j.pamj.20180704.11

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On a Subclass of P-Valent Functions Defined by a Generalized Salagean Operator

Ozokeraha Christiana Funmilayo

Published in Pure and Applied Mathematics Journal (Volume 7, Issue 4)

Received: 31 July 2018 Accepted: 18 September 2018 Published: 6 November 2018

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Abstract

In recent times, the study of analytic functions has been useful in solving many problems in mechanics, Laplace equation, electrostatics, etc. An analytic function is said to be univalent in a domain if it does not take the same value twice in that domain while an analytic function is said to be p-valent in a domain if it does not take the same value more than p times in that domain. Many researches on properties of p-valent functions using Salagean, Al Oboudi and Opoola differential operators have been reviewed. The aim of this research is to obtain the properties of new subclasses of p-valent functions defined by Salagean differential operator and its objectives are to obtain new subclasses of p-valent functions and the necessary properties for the new subclasses. This research will be a contribution to knowledge in geometric function theory and provide new tools of applications in fluid dynamics and differential equations. This paper introduces new subclasses of p – valent functions defined by Al –Oboudi differential operator. Finally, the paper studies some interesting results including subordination, coefficient inequalities, starlikeness and convexity conditions, Hadamard product and certain properties of neighbourhoods of the new subclasses of p-valent functions. Theorems were used to establish certain conditions of the new subclasses of p-valent functions.

Published in	Pure and Applied Mathematics Journal (Volume 7, Issue 4)
DOI	10.11648/j.pamj.20180704.11
Page(s)	45-62
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), 2018. Published by Science Publishing Group

Keywords

P-Valent Functions, Analytic Functions, Differential Operator, Subordination

References

[1]	Al - Oboudi, F. M. and Haidan, M. M. (2000), Spiralike Functions of Complex Order. J. Nat. Geom. Vol. 19. pp. 53 – 72.
[2]	Al - Oboudi, F. M. (2004), On Univalent Functions Defined by a Generalized Salagean Operator. International Journal of Mathematics and Mathematical Sciences. Vol. 27. pp. 1429 – 1436.
[3]	Aouf, M. K., Hossen, H. M., Srivastava, H. M. (2000), Some Families of Multivalent Functions. Applied Mathematics and Computation. Vol. 39. pp. 39 -48
[4]	Aouf, M. K., Al - Oboudi, F. M. and Haidan, M. M. (2005), On some Results for λ-Spiralike and λ-Robertson Functions of Complex Order. Publ. Instit. Math. Belgrade. Vol. 77. pp. 93 – 98.
[5]	Babalola, K. O. and Opoola, P. O. (2006) Integrated Integral Transform of Caratheodory Functions and their Applications to Analytic andUnivalent Functions Tamkang J. Math. 37(4) 355 – 366
[6]	Bulut, S. (2010), On a Class of Analytic and Multivalent Functions with Negative Coefficients Defined by Al-Oboudi Differential Operator. Studia Univ. “Babes – Bolyai” Mathematica. Vol. LV. No. 4. pp. 115 - 130
[7]	Dileep, L. and Latha, S. (2012) On P – valent Functions of Complex Order. Demonstratio Mathematica. Vol. XLV. No. 3 pp. 541 – 547.
[8]	Fadipe Joseph, O. A. and Opoola, T. O. (2010), On P-valent Functions. ICASTOR. Journal of Mathematical Sciences. Vol. 4. No. 1. pp. 83 – 86.
[9]	Fadipe Joseph, O. A. Moses, B. O. and Opoola, T. O. (2015), Multivalence of the Bessel Functions. IEJPAM. Vol. 9. No. 2. pp. 95 – 104.
[10]	Mahzoon, H. (2011), On Certain Subclasses of Analytic Functions Defined by Differential Subordination. International Journal of Mathematics and Mathematical Sciences. Vol. 2011. pp. 1 – 10.
[11]	Makinde, D. O. and Opoola, T. O. (2013) On Starlikeness and Convexity Properties of certain Subclass of Funtions. International Journal of Scientific and Research Publication 3(4) 1 – 3.
[12]	Mostafa, A. O. and Aouf, M. K. (2009) Neighbourhoods of Certain P – valent Analytic Functions with Complex Order. Computers and Mathematics with Applications. Vol. 58. pp. 1183 – 1189.
[13]	Noor, K. I. (2005), On Classes of Analytic Functions Defined by Convolution with Incomplete Beta Functions. J. Math. Anal. Appl Vol. 307. pp. 339 – 349.
[14]	Noor, K. I., Mustafa, S., Malik, B. (2009), On some classes of P – valently functions Involving certain Carlson Shaffer Operator. Applied Mathematics and Computation. Vol. 214. pp. 336 -341.
[15]	Noor, K. I., Bukhari, S. Z. H., Arif, M. and Nazir, M. (2013), Some Propertiesof P – valent functions Involving Cho – Kwon – SrivastavaIntegral Operator. Journal of Classical Analysis. Vol. 3. No. 1. pp. 35 – 43.
[16]	Opoola, T. O. (2017) On a Subclass of Univalent Functions defined by a Generalized Differential Operator. International Journal of Mathematical Analysis. Vol. 11. No. 18. pp. 869 – 876.
[17]	Oyekan, E. A. and Opoola, T. O. (2014), On Subordination for Analytic Functions defined by Convolution. Annales Universitatis Marie Curie – Skiodowska Lubli – Poloma. Vol. LXVIII. No. 1. pp. 1 – 8.
[18]	Salagean, G. S. (1983), Subclass of Univalent Functions. Lect. Notes. Math. (Springer – Verlag). 1013. 362 – 372.
[19]	Sezgin, Akbulut, Ekrem, Kadioglu, and Murat, Ozdemir (2004), On the Subclass of P – valently functions. Applied Mathematics and Computation. Vol. 147. pp. 89 – 96.

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Ozokeraha Christiana Funmilayo. (2018). On a Subclass of P-Valent Functions Defined by a Generalized Salagean Operator. Pure and Applied Mathematics Journal, 7(4), 45-62. https://doi.org/10.11648/j.pamj.20180704.11

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ACS Style

Ozokeraha Christiana Funmilayo. On a Subclass of P-Valent Functions Defined by a Generalized Salagean Operator. Pure Appl. Math. J. 2018, 7(4), 45-62. doi: 10.11648/j.pamj.20180704.11

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AMA Style

Ozokeraha Christiana Funmilayo. On a Subclass of P-Valent Functions Defined by a Generalized Salagean Operator. Pure Appl Math J. 2018;7(4):45-62. doi: 10.11648/j.pamj.20180704.11

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@article{10.11648/j.pamj.20180704.11,
  author = {Ozokeraha Christiana Funmilayo},
  title = {On a Subclass of P-Valent Functions Defined by a Generalized Salagean Operator},
  journal = {Pure and Applied Mathematics Journal},
  volume = {7},
  number = {4},
  pages = {45-62},
  doi = {10.11648/j.pamj.20180704.11},
  url = {https://doi.org/10.11648/j.pamj.20180704.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20180704.11},
  abstract = {In recent times, the study of analytic functions has been useful in solving many problems in mechanics, Laplace equation, electrostatics, etc. An analytic function is said to be univalent in a domain if it does not take the same value twice in that domain while an analytic function is said to be p-valent in a domain if it does not take the same value more than p times in that domain. Many researches on properties of p-valent functions using Salagean, Al Oboudi and Opoola differential operators have been reviewed. The aim of this research is to obtain the properties of new subclasses of p-valent functions defined by Salagean differential operator and its objectives are to obtain new subclasses of p-valent functions and the necessary properties for the new subclasses. This research will be a contribution to knowledge in geometric function theory and provide new tools of applications in fluid dynamics and differential equations. This paper introduces new subclasses of p – valent functions defined by Al –Oboudi differential operator. Finally, the paper studies some interesting results including subordination, coefficient inequalities, starlikeness and convexity conditions, Hadamard product and certain properties of neighbourhoods of the new subclasses of p-valent functions. Theorems were used to establish certain conditions of the new subclasses of p-valent functions.},
 year = {2018}
}

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TY  - JOUR
T1  - On a Subclass of P-Valent Functions Defined by a Generalized Salagean Operator
AU  - Ozokeraha Christiana Funmilayo
Y1  - 2018/11/06
PY  - 2018
N1  - https://doi.org/10.11648/j.pamj.20180704.11
DO  - 10.11648/j.pamj.20180704.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 45
EP  - 62
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20180704.11
AB  - In recent times, the study of analytic functions has been useful in solving many problems in mechanics, Laplace equation, electrostatics, etc. An analytic function is said to be univalent in a domain if it does not take the same value twice in that domain while an analytic function is said to be p-valent in a domain if it does not take the same value more than p times in that domain. Many researches on properties of p-valent functions using Salagean, Al Oboudi and Opoola differential operators have been reviewed. The aim of this research is to obtain the properties of new subclasses of p-valent functions defined by Salagean differential operator and its objectives are to obtain new subclasses of p-valent functions and the necessary properties for the new subclasses. This research will be a contribution to knowledge in geometric function theory and provide new tools of applications in fluid dynamics and differential equations. This paper introduces new subclasses of p – valent functions defined by Al –Oboudi differential operator. Finally, the paper studies some interesting results including subordination, coefficient inequalities, starlikeness and convexity conditions, Hadamard product and certain properties of neighbourhoods of the new subclasses of p-valent functions. Theorems were used to establish certain conditions of the new subclasses of p-valent functions.
VL  - 7
IS  - 4
ER  -

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Author Information

Ozokeraha Christiana Funmilayo

Department of Statistics, Delta State Polytechnic, Oghara, Nigeria

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Plain Text BibTeX RIS

APA Style

Ozokeraha Christiana Funmilayo. (2018). On a Subclass of P-Valent Functions Defined by a Generalized Salagean Operator. Pure and Applied Mathematics Journal, 7(4), 45-62. https://doi.org/10.11648/j.pamj.20180704.11

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ACS Style

Ozokeraha Christiana Funmilayo. On a Subclass of P-Valent Functions Defined by a Generalized Salagean Operator. Pure Appl. Math. J. 2018, 7(4), 45-62. doi: 10.11648/j.pamj.20180704.11

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AMA Style

Ozokeraha Christiana Funmilayo. On a Subclass of P-Valent Functions Defined by a Generalized Salagean Operator. Pure Appl Math J. 2018;7(4):45-62. doi: 10.11648/j.pamj.20180704.11

Copy | Download

@article{10.11648/j.pamj.20180704.11,
  author = {Ozokeraha Christiana Funmilayo},
  title = {On a Subclass of P-Valent Functions Defined by a Generalized Salagean Operator},
  journal = {Pure and Applied Mathematics Journal},
  volume = {7},
  number = {4},
  pages = {45-62},
  doi = {10.11648/j.pamj.20180704.11},
  url = {https://doi.org/10.11648/j.pamj.20180704.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20180704.11},
  abstract = {In recent times, the study of analytic functions has been useful in solving many problems in mechanics, Laplace equation, electrostatics, etc. An analytic function is said to be univalent in a domain if it does not take the same value twice in that domain while an analytic function is said to be p-valent in a domain if it does not take the same value more than p times in that domain. Many researches on properties of p-valent functions using Salagean, Al Oboudi and Opoola differential operators have been reviewed. The aim of this research is to obtain the properties of new subclasses of p-valent functions defined by Salagean differential operator and its objectives are to obtain new subclasses of p-valent functions and the necessary properties for the new subclasses. This research will be a contribution to knowledge in geometric function theory and provide new tools of applications in fluid dynamics and differential equations. This paper introduces new subclasses of p – valent functions defined by Al –Oboudi differential operator. Finally, the paper studies some interesting results including subordination, coefficient inequalities, starlikeness and convexity conditions, Hadamard product and certain properties of neighbourhoods of the new subclasses of p-valent functions. Theorems were used to establish certain conditions of the new subclasses of p-valent functions.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - On a Subclass of P-Valent Functions Defined by a Generalized Salagean Operator
AU  - Ozokeraha Christiana Funmilayo
Y1  - 2018/11/06
PY  - 2018
N1  - https://doi.org/10.11648/j.pamj.20180704.11
DO  - 10.11648/j.pamj.20180704.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 45
EP  - 62
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20180704.11
AB  - In recent times, the study of analytic functions has been useful in solving many problems in mechanics, Laplace equation, electrostatics, etc. An analytic function is said to be univalent in a domain if it does not take the same value twice in that domain while an analytic function is said to be p-valent in a domain if it does not take the same value more than p times in that domain. Many researches on properties of p-valent functions using Salagean, Al Oboudi and Opoola differential operators have been reviewed. The aim of this research is to obtain the properties of new subclasses of p-valent functions defined by Salagean differential operator and its objectives are to obtain new subclasses of p-valent functions and the necessary properties for the new subclasses. This research will be a contribution to knowledge in geometric function theory and provide new tools of applications in fluid dynamics and differential equations. This paper introduces new subclasses of p – valent functions defined by Al –Oboudi differential operator. Finally, the paper studies some interesting results including subordination, coefficient inequalities, starlikeness and convexity conditions, Hadamard product and certain properties of neighbourhoods of the new subclasses of p-valent functions. Theorems were used to establish certain conditions of the new subclasses of p-valent functions.
VL  - 7
IS  - 4
ER  -

Copy | Download