- Ahmad, M.S., Mehmood, Q., Nazeer, W. and Haq, A.U., (2015), An application of a Hypergeometric distribution series on certain analytic functions, Sci. Int.(Lahore), 27(4), pp. 2989-2992.
- Ahmad, D., (2014), Mapping properties of some convolution operator associated with some special function, M.Phil. Dissertation, C.S.J.M. University, Kanpur, India.
- Ahuja, O.P., (2008), Connections between various subclasses of planar harmonic mappings involving hypergeometric functions, Appl. Math. Comput., 198 (1), pp. 305-316.
- Ahuja, O.P., and Jahangiri, J.M., (2002), Noshiro-type harmonic univalent functions, Sci. Math. Jpn., (2), pp. 253-259.
- Altinkaya, S. and Yalcin, S., (2018), Poisson distribution series for analytic univalent functions, Com- plex Anal. Oper. Theory, 12(5), pp. 1315-1319.
- Altinkaya, S. and Yalcin, S., (2017), Poisson distribution series for certain subclasses of starlike func- tions with negative coefficients, Annal. Oradea Univ. Math. Fasci., 24 (2), pp. 5-8.
- Clunie, J. and Sheil-Small, T., (1984), Harmonic univalent functions, Ann. Acad. Sci. Fen. Series A.I. Math., 9, pp. 3-25.
- Duren, P., (2004), Harmonic mappings in the plane, Vol. 156, Cambridge University Press, Cambridge.
- Mondal, S.R. and Swaminathan, A., (2012), Geometric properties of Generalized Bessel functions
- Bull. Malays. Math. Sci. Soc., 35(1), pp. 179-194. Murugusundaramoorthy, G., Vijaya, K. and Porwal, S., (2016), Some inclusion results of certain subclasses of analytic functions associated with Poisson distribution series, Hacettepe J. Math. Stat., (4), pp. 1101-1107.
- Ponnusamy, S. and Rİnning, F., (1998), Starlikeness properties for convolution involving hypergeo- metric series, Ann. Univ. Mariae Curie-Sklodowska, LII, 1(16), pp. 141-155.
- Porwal, S., (2014), An application of a Poisson distribution series on certain analytic functions, J.Complex Anal., Art. ID 984135, pp. 1-3.
- Porwal, S., (2015), Some connections between various subclasses of planar harmonic mappings involv- ing generalized Bessel functions, Afr. Mat., 26(5-6), pp. 997-1008.
- Porwal, S. and Kumar, M., (2016), A unified study on starlike and convex functions associated with Poisson distribution series, Afr. Mat., 27(5-6), pp. 1021-1027.
- Porwal, S. and Kumar, S., (2017), Confluent hypergeometric distribution and its applications on certain classes of univalent functions, Afr. Mat., 28, pp. 1-8.
- Porwal, S. and Srivastava, D., (2017), Harmonic starlikeness and convexity of integral operators generated by Poisson distribution series, Math. Moravica, 21, pp. 51-60.
- Rosy, T., Stephen, B.A., Subramanian, K.G. and Jahangiri, J.M., (2001), Goodman-Rİnning-type harmonic univalent functions, Kyungpook Math. J., 41 (1), pp. 45-54.
- Sharma, A.K., Porwal, S. and Dixit, K.K., (2013), Class mappings properties of convolutions involving certain univalent functions associated with hypergeometric functions, Electronic J. Math. Anal. Appl., (2), pp. 326-333
- Yalcin, S., ¨Ozt¨urk, M., and Yamankaradeniz, M., (2007), On subclass of Salagean-type harmonic univalent functions, J. Inequal. Pure Appl. Math., 8 (2), Art. 54, pp. 1-9.

The purpose of the present paper is to establish connections between various subclasses of harmonic univalent functions by applying certain convolution operator involving Confluent Hypergeometric distribution series. To be more precise, we investigate such connections with Goodman-Ronning-type harmonic univalent functions in the open unit disc U.

- Ahmad, M.S., Mehmood, Q., Nazeer, W. and Haq, A.U., (2015), An application of a Hypergeometric distribution series on certain analytic functions, Sci. Int.(Lahore), 27(4), pp. 2989-2992.
- Ahmad, D., (2014), Mapping properties of some convolution operator associated with some special function, M.Phil. Dissertation, C.S.J.M. University, Kanpur, India.
- Ahuja, O.P., (2008), Connections between various subclasses of planar harmonic mappings involving hypergeometric functions, Appl. Math. Comput., 198 (1), pp. 305-316.
- Ahuja, O.P., and Jahangiri, J.M., (2002), Noshiro-type harmonic univalent functions, Sci. Math. Jpn., (2), pp. 253-259.
- Altinkaya, S. and Yalcin, S., (2018), Poisson distribution series for analytic univalent functions, Com- plex Anal. Oper. Theory, 12(5), pp. 1315-1319.
- Altinkaya, S. and Yalcin, S., (2017), Poisson distribution series for certain subclasses of starlike func- tions with negative coefficients, Annal. Oradea Univ. Math. Fasci., 24 (2), pp. 5-8.
- Clunie, J. and Sheil-Small, T., (1984), Harmonic univalent functions, Ann. Acad. Sci. Fen. Series A.I. Math., 9, pp. 3-25.
- Duren, P., (2004), Harmonic mappings in the plane, Vol. 156, Cambridge University Press, Cambridge.
- Mondal, S.R. and Swaminathan, A., (2012), Geometric properties of Generalized Bessel functions
- Bull. Malays. Math. Sci. Soc., 35(1), pp. 179-194. Murugusundaramoorthy, G., Vijaya, K. and Porwal, S., (2016), Some inclusion results of certain subclasses of analytic functions associated with Poisson distribution series, Hacettepe J. Math. Stat., (4), pp. 1101-1107.
- Ponnusamy, S. and Rİnning, F., (1998), Starlikeness properties for convolution involving hypergeo- metric series, Ann. Univ. Mariae Curie-Sklodowska, LII, 1(16), pp. 141-155.
- Porwal, S., (2014), An application of a Poisson distribution series on certain analytic functions, J.Complex Anal., Art. ID 984135, pp. 1-3.
- Porwal, S., (2015), Some connections between various subclasses of planar harmonic mappings involv- ing generalized Bessel functions, Afr. Mat., 26(5-6), pp. 997-1008.
- Porwal, S. and Kumar, M., (2016), A unified study on starlike and convex functions associated with Poisson distribution series, Afr. Mat., 27(5-6), pp. 1021-1027.
- Porwal, S. and Kumar, S., (2017), Confluent hypergeometric distribution and its applications on certain classes of univalent functions, Afr. Mat., 28, pp. 1-8.
- Porwal, S. and Srivastava, D., (2017), Harmonic starlikeness and convexity of integral operators generated by Poisson distribution series, Math. Moravica, 21, pp. 51-60.
- Rosy, T., Stephen, B.A., Subramanian, K.G. and Jahangiri, J.M., (2001), Goodman-Rİnning-type harmonic univalent functions, Kyungpook Math. J., 41 (1), pp. 45-54.
- Sharma, A.K., Porwal, S. and Dixit, K.K., (2013), Class mappings properties of convolutions involving certain univalent functions associated with hypergeometric functions, Electronic J. Math. Anal. Appl., (2), pp. 326-333
- Yalcin, S., ¨Ozt¨urk, M., and Yamankaradeniz, M., (2007), On subclass of Salagean-type harmonic univalent functions, J. Inequal. Pure Appl. Math., 8 (2), Art. 54, pp. 1-9.

Primary Language | English |
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Journal Section | Research Article |

Authors | |

Publication Date | December 1, 2019 |

Published in Issue | Year 2019 Volume: 9 Issue: 4 |

Bibtex | @ { twmsjaem760965, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2019}, volume = {9}, number = {4}, pages = {921 - 929}, title = {SOME INCLUSION RELATIONS BETWEEN VARIOUS SUBCLASSES OF PLANAR HARMONIC MAPPINGS INVOLVING CONFLUENT HYPERGEOMETRIC DISTRIBUTION SERIES}, key = {cite}, author = {Porwal, S.} } |