On Janowski type harmonic functions associated with the Wright hypergeometric functions

Автор: Murugusundaramoorthy Gangadharan, Porwal Saurabh

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 4 т.25, 2023 года.

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In our present study we consider Janowski type harmonic functions class introduced and studied by Dziok, whose members are given by h(z)=z+∑∞n=2hnzn and g(z)=∑∞n=1gnzn, such that STH(F,G)={f=h+g¯∈H:DHf(z)f(z) ≺ 1+Fz1+Gz;(-G ≤ F

Harmonic functions, univalent functions, wright's generalized hypergeometric functions

Короткий адрес: https://sciup.org/143180942

IDR: 143180942   |   DOI: 10.46698/b2503-7977-9793-e

Список литературы On Janowski type harmonic functions associated with the Wright hypergeometric functions

  • Clunie, J. and Sheil-Small, T. Harmonic Univalent Functions, Annales Academiae Scientiarum Fennicae, Series A I, Mathematica, 1984, vol. 9, pp. 3-25.
  • Duren, P. Harmonic Mappings in the Plane, Cambridge Tracts in Mathematics, 156, Cambridge, Cambridge University Press, 2004. DOI: 10.1017/CBO9780511546600.
  • Ahuja, Om. P. Planar Harmonic Univalent and Related Mappings, Journal of Inequalities in Pure and Applied Mathematics, 2005, vol. 6, no. 4, Article 122, 18 p.
  • Silverman, H. Harmonic Univalent Functions with Negative Coefficients, Journal of Mathematical Analysis and Applications, 1998, vol. 220, pp. 283-289. DOI: 10.1006/jmaa.1997.5882.
  • Wright, E. M. The Asymptotic Expansion of the Generalized Hypergeometric Function, Proceedings of the London Mathematical Society, 1940, vol. s2-46, no. 1, pp. 389-408. DOI: 10.1112/plms/s2-46.1.389.
  • Srivastava, H. M. Some Fox-Wright Generalized Hypergeometric Functions and Associated Families of Convolution Operators, Applicable Analysis and Discrete Mathematics, 2007, vol. 1, no. 1, pp. 56-71.
  • Srivastava, H. M. and Manocha, H. L. A Treatise on Generating Functions, Ellis Horwood Series: Mathematics and its Applications, Chichester, Ellis Horwood Ltd., 1984.
  • Dziok, J. and Srivastava, H. M. Certain Subclasses of Analytic Functions Associated with the Generalized Hypergeometric Function, Integral Transforms and Special Functions, 2003, vol. 14, no. 1, pp. 7-18. DOI: 10.1080/10652460304543.
  • Themangani R., Porwal, S. and Magesh, N. Inclusion Relation Between Various Subclasses of Harmonic Univalent Functions Associated with the Wright's Generalized Hypergeometric Functions, Abstract and Applied Analysis, 2020, vol. 2020, Article ID 8811810, pp. 1-6. DOI: 10.1155/2020/8811810.
  • Dziok, J. On Janowski Harmonic Functions, Journal of Applied Analysis, 2015, vol. 21, no. 2, pp. 99-107. DOI: 10.1515/jaa-2015-0010.
  • Janowski, W. Some Extremal Problems For Certain Families Of Analytic Functions I, Annales Polonici Mathematici, 1973, vol. 28, pp. 297-326.
  • Jahangiri, J. M. Coefficient Bounds and Univalence Criteria for Harmonic Functions with Negative Coefficients, Annales Universitatis Mariae Curie-Sklodowska, sectio A -- Mathematica, 1998, vol. 52, no. 2, pp. 57-66.
  • Jahangiri, J. M. Harmonic Functions Starlike in the Unit Disk, Journal of Mathematical Analysis and Applications, 1999, vol. 235, pp. 470-477. DOI: 10.1006/jmaa.1999.6377.
  • Ahuja, Om. P. Connections Between Various Subclasses of Planar Harmonic Mappings Involving Hypergeometric Functions, Applied Mathematics and Computation, 2008, vol. 198, no. 1, pp. 305-316. DOI: 10.1016/j.amc.2007.08.035.
  • Ponnusamy, S. and Ronning, F. Starlikeness Properties for Convolutions Involving Hypergeometric Series, Annales Universitatis Mariae Curie-Sklodowska, sectio A -- Mathematica, 1998, vol. 52, no. 1, pp. 141-155.
  • Porwal, S. and Dixit, K. K. An Application of Hypergeometric Functions on Harmonic Univalent Functions, Bulletin of Mathematical Analysis and Applications, 2010, vol. 2, no. 4, pp. 97-105.
  • Miller, S. S. and Mocanu, P. T. Univalence of Gaussian and Confluent Hypergeometric Functions, Proceedings of the American Mathematical Society, 1990, vol. 110, no. 2, pp. 333-342.
  • Owa, S. and Srivastava, H. M. Univalent and Starlike Generalized Hypergeometric Functions, Canadian Journal of Mathematics, 1987, vol. 39, no. 5, pp. 1057-1077.
  • Aouf, M. K. and Dziok, J. Distortion and Convolution Theorems for Operators of Generalized Fractional Calculus Involving Wright Function, Journal of Applied Analysis, 2008, vol. 14, no. 2, pp. 183-192. DOI: 10.1515/JAA.2008.183.
  • Murugusundaramoorthy, G. and Raina, R. K. On a Subclass of Harmonic Functions Associated with Wright's Generalized Hypergeometric Functions, Synthesis Lectures on Mathematics and Statistics, 2009, vol. 38, no. 2, pp. 129-136.
  • Raina, R. K. and Sharma, P. Harmonic Univalent Functions Associated with Wright's Generalized Hypergeometric Functions, Integral Transforms and Special Functions, 2011, vol. 22, no. 8, pp. 561-572. DOI: 10.1080/10652469.2010.535797.
  • Raina, R. K. and Nahar, T. S. On Characterization of Certain Wright's Generalized Hypergeometric Functions Involving Certain Subclasses of Analytic Functions, Informatica, Vilnius, Institute of Mathematics and Informatics, 1999, vol. 10, no. 2, pp. 219-230.
  • Chaurasia, V. B. L. and Parihar, H. S. Certain Sufficiency Conditions on Fox-Wright Functions, Demonstratio Mathematica, 2008, vol. 41, no. 4, pp. 813-822. DOI: 10.1515/dema-2008-0409.
  • Attiya, A. A. Some Applications of Mittag-Leffler Function in the Unit Disk, Filomat, 2016, vol. 30, no. 7, pp. 2075-2081. DOI: 10.2298/FIL1607075A.
  • Porwal, S. Connections Between Various Subclasses of Planar Harmonic Mappings Involving Generalized Bessel Functions, Thai Journal of Mathematics, 2015, vol. 13, no. 1, pp. 33-42.
  • Maharana, S. and Sahoo, S. K. Inclusion Properties of Planar Harmonic Mappings Associated with the Wright Function, Complex Variables and Elliptic Equations, 2020, vol. 66, no. 10, pp. 1619-1641. DOI: 10.1080/17476933.2020.1772765.
  • Vijaya, K., Dutta, H. and Murugusundaramoorthy, G. Inclusion Relation Between Subclasses of Harmonic Functions Associated with Mittag-LeffEr Functions, Mathematics in Engineering, Science and Aerospace, 2020, vol. 11, no. 4, pp. 959-968.
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