Research Article
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Application of neutrosophic Poisson distribution series on harmonic classes of analytic functions defined by q− derivative operator and sigmoid function

Year 2024, Volume: 73 Issue: 4, 997 - 1010, 30.12.2024

Ibrahim Tunji Awolere , Abiodun Oladipo , Şahsene Altınkaya

https://doi.org/10.31801/cfsuasmas.1483387

Abstract

There are several authors who have obtained various forms of properties for some subclasses of analytic univalent functions related to different distribution series, such as Binomial, Generalized Discrete Probability, Geometric, Mittag-Leffler, Pascal, and Poisson distribution series. The authors, in this paper, proved the inclusion relation of the harmonic analytic function class $H_{q}^{\alpha}(\theta, \gamma(s), \Psi)$ established by applying convolution operators regarding neutrosophic distribution series equipped with the Sigmoid function (activation function). The present results are capable of handling both accurate (determinate) data and inaccurate (indeterminate) data.

Keywords

Analytic harmonic starlike harmonic convex neutrosophic Poisson distribution q-derivative

References

  • Ahuja, O. P., Jahangiri, J. M., A subclass of harmonic univalent functions, J. Nat. Geom., 20 (2001), 45–56.
  • Ahuja, O. P., C¸ etinkaya, A., Use of quantum calculus approach in mathematical sciences and its role in geometric function theory, AIP Conference Proceedings, 2095(1) (2019), 1-14. https://doi.org/10.1063/1.5097511
  • Ahuja, O. P., Jahangiri, J. M., Noshiro-type harmonic univalent functions, Sci. Math. Jpn., 6 (2002), 253–259.
  • Alhabib, R., Ranna, M. M., Farah, H., Salama, A. A., Some nuetrosophic probability distributions, Neutrosophic Sets Syst., 22 (2018), 30–37.
  • Awolere, I. T., Oladipo, A. T., Application of neutrosophic Poisson probability distribution series for certain subclass of analytic univalent function, TWMS J. App. and Eng. Math., 13(3) (2023), 1042-1052.
  • Awolere, I. T., Hankel determinant for bi-Bazelevic function involing error and sigmoid function defined by derivative calculus via Chebyshev polynomials, J. Frac. Calc. Appl., 11(2) (2020), 208-217.
  • Aydogan, M., Bshouty, D., Lyzzaik, A., Sakar, F. M., On the shears of univalent harmonic mappings, Complex Anal. Oper. Theory, 13 (2019), 2853-2862. https://doi.org/10.1007/s11785-018-0855-9
  • Bayram, H., q-Analogue of a new subclass of harmonic univalent functions associated with subordination, Symmetry, 14 (2022), 1-15. https://doi.org/10.3390/sym14040708
  • Bshouty, D., Lyzzaik, A., Sakar, F. M., Harmonic mappings of bounded boundary ratation, Proc. Am. Math. Soc., 146 (2018), 1113-1221. http://dx.doi.org/10.1090/proc/13796
  • Chandrashekar, R., Lee, S. K., Subramanian, K. G., Hyergeometric functions and subclasses of harmonic mappings, Proceeding of the International Conference on Mathematical Analysis, 2010, Bangkok, 2010, 95–103.
  • Clunie, J., Sheil-Small, T., Harmonic univalent functions, Ann. Acad. Sci. Fen., 9 (1984), 3–25.
  • Duren, P., Harmonic Mappings in Plane, Cambridge Tracts in Mathematics; Cambridge University Press: Cambridge UK, 156, 2004.
  • Frasin, B. A., Comprehensive family of harmonic univalent functions, SUT J. Math., 42 (2006), 145-155. http://dx.doi.org/10.55937/sut/1159988041
  • Frasin, B. A., Alb Lupas, A., An application of Poisson distribution series on harmonic classes of analytic functions, Symmetry, 15(3) (2023), 1-11. https://doi.org/10.3390/sym15030590
  • Jackson, F. H., On q-definite integrals, Quart. J. Pure Appl. Math., 14 (1910), 193-203. https://doi.org/10.1080/14786447108640600
  • Jackson, F.H., On q-functions and a certain difference operator, Earth Environ. Sci. Trans. R. Soc. Edinb., 46(2) (1908), 253–281. https://doi.org/10.1017/S0080456800002751
  • Jahangiri, J. M., Harmonic functions starlike in the unit disk, J. Math. Anal. Appl., 235(2) (1999), 470-477. https://doi.org/10.1006/jmaa.1999.6377
  • Murugusundaramoorthy, G., Vijaya, K., Frasin, B. A., A subclass of harmonic funtion with negative coefficients defined by Dziok-Srivastava operator, Tamkang J. Math., 42(4) (2011), 463-473. https://doi.org/10.5556/j.tkjm.42.2011.231
  • Oladipo, A. T., Gbolagade, A. M., Some subordination results for logistic sigmoid activation function in the space of univalent functions, Adv. Comput. Sci. Eng., 12 (2014), 61-79.
  • Oladipo, A. T., Coefficient inequality for a subclass of analytic univalent functions related to simple logistic functions, Stud. Univ. Babes-Bolyai Math., 61(1) (2016), 45-52.
  • Oladipo, A. T., Bounds for Poisson and neutrosophic Poisson distribution associated with Chebyshev polynomials, Palest. J. Math., 10(1) (2019), 169–174.
  • Porwal, S., Srivastava, D., Some connections between various classes of planar harmonic mappings involving Poisson distribution series, Electronic J. Math. Anai. Appl., 6(2) (2018), 163-171.
  • Silverman, H., Harmonic univalent function with negative coefficients, J. Math. Anal. Appl., 220(1) (1998), 283–289. https://doi.org/10.1006/jmaa.1997.5882
  • Silverman, H., Silvia, E. M., Subclasses of harmonic univalent functions, New Zealand J. Math., 28 (1999), 275-284.
  • Smarandache, F., Khalid, H. E., Neutrosophic Precalculus and Neutrosophic Calculus: Neutrosophic Applications, Infinite Study, PONS, Stuttgart, Germany, 2nd edition, 2018.
  • Sokol, J., Ibrahim, R. W., Ahmad, M. Z., Al-Janaby, H. F., Inequalities of harmonic univalent functions with connections of hypergeometric functions, Open Math., 13 (2015), 691–705. https://doi.org/10.1515/math-2015-0066
  • Srivastava, H. M., Khan, N. Khan, S., Ahmad, Q. Z., Khan, B., A Class of k-symmetric harmonic functions involving a certain q-derivative operator, Mathematics, 9(15) (2021), 1-14. https://doi.org/10.3390/math9151812
  • Yalçın, S., Öztürk, M., Yamankaradeniz, M., A subclass of harmonic univalent functions with negative coefficients, Appl. Math. Comput., 142(2-3) (2003), 469-–476. https://doi.org/10.1016/S0096-3003(02)00314-4
  • Yalçın, S., Öztürk, M., A new subclass of complex harmonic functions, Math. Inequal. Appl., 7(1) (2004), 55–61.
  • Yousef, A. T., Salleh, Z., On a harmonic univalent subclass of functions involving a generalized linear operator, Axioms, 9(1) (2020), 1-10. https://doi.org/10.3390/axioms9010032

Year 2024, Volume: 73 Issue: 4, 997 - 1010, 30.12.2024

Ibrahim Tunji Awolere , Abiodun Oladipo , Şahsene Altınkaya

https://doi.org/10.31801/cfsuasmas.1483387

Abstract

References

  • Ahuja, O. P., Jahangiri, J. M., A subclass of harmonic univalent functions, J. Nat. Geom., 20 (2001), 45–56.
  • Ahuja, O. P., C¸ etinkaya, A., Use of quantum calculus approach in mathematical sciences and its role in geometric function theory, AIP Conference Proceedings, 2095(1) (2019), 1-14. https://doi.org/10.1063/1.5097511
  • Ahuja, O. P., Jahangiri, J. M., Noshiro-type harmonic univalent functions, Sci. Math. Jpn., 6 (2002), 253–259.
  • Alhabib, R., Ranna, M. M., Farah, H., Salama, A. A., Some nuetrosophic probability distributions, Neutrosophic Sets Syst., 22 (2018), 30–37.
  • Awolere, I. T., Oladipo, A. T., Application of neutrosophic Poisson probability distribution series for certain subclass of analytic univalent function, TWMS J. App. and Eng. Math., 13(3) (2023), 1042-1052.
  • Awolere, I. T., Hankel determinant for bi-Bazelevic function involing error and sigmoid function defined by derivative calculus via Chebyshev polynomials, J. Frac. Calc. Appl., 11(2) (2020), 208-217.
  • Aydogan, M., Bshouty, D., Lyzzaik, A., Sakar, F. M., On the shears of univalent harmonic mappings, Complex Anal. Oper. Theory, 13 (2019), 2853-2862. https://doi.org/10.1007/s11785-018-0855-9
  • Bayram, H., q-Analogue of a new subclass of harmonic univalent functions associated with subordination, Symmetry, 14 (2022), 1-15. https://doi.org/10.3390/sym14040708
  • Bshouty, D., Lyzzaik, A., Sakar, F. M., Harmonic mappings of bounded boundary ratation, Proc. Am. Math. Soc., 146 (2018), 1113-1221. http://dx.doi.org/10.1090/proc/13796
  • Chandrashekar, R., Lee, S. K., Subramanian, K. G., Hyergeometric functions and subclasses of harmonic mappings, Proceeding of the International Conference on Mathematical Analysis, 2010, Bangkok, 2010, 95–103.
  • Clunie, J., Sheil-Small, T., Harmonic univalent functions, Ann. Acad. Sci. Fen., 9 (1984), 3–25.
  • Duren, P., Harmonic Mappings in Plane, Cambridge Tracts in Mathematics; Cambridge University Press: Cambridge UK, 156, 2004.
  • Frasin, B. A., Comprehensive family of harmonic univalent functions, SUT J. Math., 42 (2006), 145-155. http://dx.doi.org/10.55937/sut/1159988041
  • Frasin, B. A., Alb Lupas, A., An application of Poisson distribution series on harmonic classes of analytic functions, Symmetry, 15(3) (2023), 1-11. https://doi.org/10.3390/sym15030590
  • Jackson, F. H., On q-definite integrals, Quart. J. Pure Appl. Math., 14 (1910), 193-203. https://doi.org/10.1080/14786447108640600
  • Jackson, F.H., On q-functions and a certain difference operator, Earth Environ. Sci. Trans. R. Soc. Edinb., 46(2) (1908), 253–281. https://doi.org/10.1017/S0080456800002751
  • Jahangiri, J. M., Harmonic functions starlike in the unit disk, J. Math. Anal. Appl., 235(2) (1999), 470-477. https://doi.org/10.1006/jmaa.1999.6377
  • Murugusundaramoorthy, G., Vijaya, K., Frasin, B. A., A subclass of harmonic funtion with negative coefficients defined by Dziok-Srivastava operator, Tamkang J. Math., 42(4) (2011), 463-473. https://doi.org/10.5556/j.tkjm.42.2011.231
  • Oladipo, A. T., Gbolagade, A. M., Some subordination results for logistic sigmoid activation function in the space of univalent functions, Adv. Comput. Sci. Eng., 12 (2014), 61-79.
  • Oladipo, A. T., Coefficient inequality for a subclass of analytic univalent functions related to simple logistic functions, Stud. Univ. Babes-Bolyai Math., 61(1) (2016), 45-52.
  • Oladipo, A. T., Bounds for Poisson and neutrosophic Poisson distribution associated with Chebyshev polynomials, Palest. J. Math., 10(1) (2019), 169–174.
  • Porwal, S., Srivastava, D., Some connections between various classes of planar harmonic mappings involving Poisson distribution series, Electronic J. Math. Anai. Appl., 6(2) (2018), 163-171.
  • Silverman, H., Harmonic univalent function with negative coefficients, J. Math. Anal. Appl., 220(1) (1998), 283–289. https://doi.org/10.1006/jmaa.1997.5882
  • Silverman, H., Silvia, E. M., Subclasses of harmonic univalent functions, New Zealand J. Math., 28 (1999), 275-284.
  • Smarandache, F., Khalid, H. E., Neutrosophic Precalculus and Neutrosophic Calculus: Neutrosophic Applications, Infinite Study, PONS, Stuttgart, Germany, 2nd edition, 2018.
  • Sokol, J., Ibrahim, R. W., Ahmad, M. Z., Al-Janaby, H. F., Inequalities of harmonic univalent functions with connections of hypergeometric functions, Open Math., 13 (2015), 691–705. https://doi.org/10.1515/math-2015-0066
  • Srivastava, H. M., Khan, N. Khan, S., Ahmad, Q. Z., Khan, B., A Class of k-symmetric harmonic functions involving a certain q-derivative operator, Mathematics, 9(15) (2021), 1-14. https://doi.org/10.3390/math9151812
  • Yalçın, S., Öztürk, M., Yamankaradeniz, M., A subclass of harmonic univalent functions with negative coefficients, Appl. Math. Comput., 142(2-3) (2003), 469-–476. https://doi.org/10.1016/S0096-3003(02)00314-4
  • Yalçın, S., Öztürk, M., A new subclass of complex harmonic functions, Math. Inequal. Appl., 7(1) (2004), 55–61.
  • Yousef, A. T., Salleh, Z., On a harmonic univalent subclass of functions involving a generalized linear operator, Axioms, 9(1) (2020), 1-10. https://doi.org/10.3390/axioms9010032
There are 30 citations in total.

Details

Primary Language English
Subjects Real and Complex Functions (Incl. Several Variables)
Journal Section Research Articles
Authors

Ibrahim Tunji Awolere 0000-0002-0771-8037

Abiodun Oladipo 0000-0001-6472-2430

Şahsene Altınkaya 0000-0002-7950-8450

Publication Date December 30, 2024
Submission Date May 13, 2024
Acceptance Date July 5, 2024
Published in Issue Year 2024 Volume: 73 Issue: 4

Cite

APA Awolere, I. T., Oladipo, A., & Altınkaya, Ş. (2024). Application of neutrosophic Poisson distribution series on harmonic classes of analytic functions defined by q− derivative operator and sigmoid function. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(4), 997-1010. https://doi.org/10.31801/cfsuasmas.1483387
AMA Awolere IT, Oladipo A, Altınkaya Ş. Application of neutrosophic Poisson distribution series on harmonic classes of analytic functions defined by q− derivative operator and sigmoid function. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2024;73(4):997-1010. doi:10.31801/cfsuasmas.1483387
Chicago Awolere, Ibrahim Tunji, Abiodun Oladipo, and Şahsene Altınkaya. “Application of Neutrosophic Poisson Distribution Series on Harmonic Classes of Analytic Functions Defined by Q− Derivative Operator and Sigmoid Function”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, no. 4 (December 2024): 997-1010. https://doi.org/10.31801/cfsuasmas.1483387.
EndNote Awolere IT, Oladipo A, Altınkaya Ş (December 1, 2024) Application of neutrosophic Poisson distribution series on harmonic classes of analytic functions defined by q− derivative operator and sigmoid function. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 4 997–1010.
IEEE I. T. Awolere, A. Oladipo, and Ş. Altınkaya, “Application of neutrosophic Poisson distribution series on harmonic classes of analytic functions defined by q− derivative operator and sigmoid function”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 73, no. 4, pp. 997–1010, 2024, doi: 10.31801/cfsuasmas.1483387.
ISNAD Awolere, Ibrahim Tunji et al. “Application of Neutrosophic Poisson Distribution Series on Harmonic Classes of Analytic Functions Defined by Q− Derivative Operator and Sigmoid Function”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/4 (December2024), 997-1010. https://doi.org/10.31801/cfsuasmas.1483387.
JAMA Awolere IT, Oladipo A, Altınkaya Ş. Application of neutrosophic Poisson distribution series on harmonic classes of analytic functions defined by q− derivative operator and sigmoid function. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73:997–1010.
MLA Awolere, Ibrahim Tunji et al. “Application of Neutrosophic Poisson Distribution Series on Harmonic Classes of Analytic Functions Defined by Q− Derivative Operator and Sigmoid Function”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 73, no. 4, 2024, pp. 997-1010, doi:10.31801/cfsuasmas.1483387.
Vancouver Awolere IT, Oladipo A, Altınkaya Ş. Application of neutrosophic Poisson distribution series on harmonic classes of analytic functions defined by q− derivative operator and sigmoid function. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73(4):997-1010.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

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