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Initial bounds for analytic function classes characterized by certain special functions and bell numbers
DOI:
https://doi.org/10.26577/JMMCS2023v120i4a5Keywords:
Analytic function, Schwarz function, (p-q) Chebyshev polynomial, (p-q) Gegenbauer polynomial, coefficient estimate, Fekete-Szego problem, subordinationAbstract
In this work, we introduced two new classes of analytic functions dened by the involvement of Galue-type Struve function, modied error function and Bell's numbers, means of q-dierentiation and the subordination principle. Some of the upper estimates obtained are on the initial bounds and the Fekete-Szego inequality.
References
[1] Abramowitz M., Stegun I.A. (eds.). Handbook of Mathematical Functions with Formulas,
Graphs and Mathematical Tables, Dover Publications Inc., New York, (1965).
[2] Aral A., Gupta V., Agarwal R.P. Applications of q-Calculus in Operator Theory, Springer
Science+Business Media, New York, (2013).
[3] Bell E.T. Exponential polynomials, Ann. Math., 35, (1934): 258277.
[4] Bell E.T. The iterated exponential integers, Ann. Math., 39, (1938): 539557.
[5] Coman D. The radius of starlikeness for error function, Stud. Univ. Babes Bolyal Math.,
36, (1991): 1316.
66 Initial bounds for analytic function classes characterized by certain special functions . . .
[6] Elbert A., Laforgia A. The zeros of the complementary error function, Numer.
Algorithms, 49 (1-4), (2008): 153157.
[7] Jackson F.H. On q-functions and a certain dierence operator, Trans. Roy. Soc. Edinb.,
46 (2), (1908): 6472.
[8] Jahangiri J.M., Ramachandran C., Annamalai S. Fekete-Szego problem for certain
analytic functions dened by hypergeometric functions and Jacobi polynomial. J. Fract.
Calc. Appl., 9, (2018): 17.
[9] Kac V., Cheung P., Quantum Calculus, Springer-Verlag Inc., New York, (2002).
[10] Lasode A.O., Opoola T.O. On a generalized class of bi-univalent functions dened by
subordination and q-derivative operator, Open J. Math. Anal., 5 (2), (2021): 4652.
[11] Lasode A.O., Opoola T.O. Fekete-Szego estimates and second Hankel determinant for
a generalized subfamily of analytic functions dened by q-dierential operator, Gulf J.
Math., 11 (2), (2021): 3643.
[12] Lasode A.O., Opoola T.O. Some investigations on a class of analytic and univalent
functions involving q-dierentiation, Eur. J. Math. Anal., 2 (12), (2022): 19.
[13] Kumar V., Cho N.E., Ravichandran V., Srivastava H.M. Sharp coecient bounds for
starlike functions associated with the Bell numbers, Math. Slovaca., 69, 2019: 10531064.
[14] Nisar K.S., Baleanu D., Qurashi M.A. Fractional calculus and application of generalized
Struve function, SpringerPlus J., 5 (910), (2016): 13 pages.
[15] Orhan H., Yagmur N. Geometric properties of generalized struve functions. In: The
International Congress in honour of Professor H.M. Srivastava, 2326, Bursa, Turkey,
(2012).
[16] Oyekan E.A. Coecient estimates and subordination results for certain classes of
analytic functions, J. Math. Sci., 24 (2), (2013): 7586.
[17] Oyekan E.A. Certain geometric properties of functions involving Galue type Struve
function, Ann. Math. Comput. Sci., 8, (2022): 4353.
[18] Oyekan E.A., Awolere I.T. A new subclass of univalent functions connected with
convolution dened via employing a linear combination of two generalized dierential
operators involving sigmoid function, Maltepe J. Math., 2 (2), (2020): 1121.
[19] Oyekan E.A., Lasode A.O. Estimates for some classes of analytic functions associated
with Pascal distribution series, error function, Bell numbers and q-dierential operator,
Nigerian J. Math. Appl., 32, (2022): 163173.
[20] Oyekan E.A., Swamy S.R., Opoola T.O. Ruscheweyh derivative and a new generalized
operator involving convolution, Internal. J. Math. Trends Technol., 67 (1) (2021): 88
100.
E.A. Oyekan, A.O. Lasode, T.A. Olatunji 67
[21] Oyekan E.A., Ojo O.O. Some properties of a class of analytic functions dened by
convolution of two generalized dierential operators, Intern. Confer. Contemp. Dev.
Math. Sci., 23, (2021): 724742.
[22] Oyekan E.A., Terwase A.J. Certain characterizations for a class of p-valent functions
dened by Salagean dierential operator, Gen. Math. Notes, 24 (2), (2014): 19.
[23] Ramachandran K., Dhanalakshmi C., Vanitha L. Hankel determinant for a subclass of
analytic functions associated with error functions bounded by conical regions, Internat.
J. Math. Anal., 11 (2), (2017): 571581.
[24] Thomas D.K., Tuneski N., Vasudevarao A. Univalent Functions: A Primer, Walter de
Gruyter Inc., Berlin, (2018)
Graphs and Mathematical Tables, Dover Publications Inc., New York, (1965).
[2] Aral A., Gupta V., Agarwal R.P. Applications of q-Calculus in Operator Theory, Springer
Science+Business Media, New York, (2013).
[3] Bell E.T. Exponential polynomials, Ann. Math., 35, (1934): 258277.
[4] Bell E.T. The iterated exponential integers, Ann. Math., 39, (1938): 539557.
[5] Coman D. The radius of starlikeness for error function, Stud. Univ. Babes Bolyal Math.,
36, (1991): 1316.
66 Initial bounds for analytic function classes characterized by certain special functions . . .
[6] Elbert A., Laforgia A. The zeros of the complementary error function, Numer.
Algorithms, 49 (1-4), (2008): 153157.
[7] Jackson F.H. On q-functions and a certain dierence operator, Trans. Roy. Soc. Edinb.,
46 (2), (1908): 6472.
[8] Jahangiri J.M., Ramachandran C., Annamalai S. Fekete-Szego problem for certain
analytic functions dened by hypergeometric functions and Jacobi polynomial. J. Fract.
Calc. Appl., 9, (2018): 17.
[9] Kac V., Cheung P., Quantum Calculus, Springer-Verlag Inc., New York, (2002).
[10] Lasode A.O., Opoola T.O. On a generalized class of bi-univalent functions dened by
subordination and q-derivative operator, Open J. Math. Anal., 5 (2), (2021): 4652.
[11] Lasode A.O., Opoola T.O. Fekete-Szego estimates and second Hankel determinant for
a generalized subfamily of analytic functions dened by q-dierential operator, Gulf J.
Math., 11 (2), (2021): 3643.
[12] Lasode A.O., Opoola T.O. Some investigations on a class of analytic and univalent
functions involving q-dierentiation, Eur. J. Math. Anal., 2 (12), (2022): 19.
[13] Kumar V., Cho N.E., Ravichandran V., Srivastava H.M. Sharp coecient bounds for
starlike functions associated with the Bell numbers, Math. Slovaca., 69, 2019: 10531064.
[14] Nisar K.S., Baleanu D., Qurashi M.A. Fractional calculus and application of generalized
Struve function, SpringerPlus J., 5 (910), (2016): 13 pages.
[15] Orhan H., Yagmur N. Geometric properties of generalized struve functions. In: The
International Congress in honour of Professor H.M. Srivastava, 2326, Bursa, Turkey,
(2012).
[16] Oyekan E.A. Coecient estimates and subordination results for certain classes of
analytic functions, J. Math. Sci., 24 (2), (2013): 7586.
[17] Oyekan E.A. Certain geometric properties of functions involving Galue type Struve
function, Ann. Math. Comput. Sci., 8, (2022): 4353.
[18] Oyekan E.A., Awolere I.T. A new subclass of univalent functions connected with
convolution dened via employing a linear combination of two generalized dierential
operators involving sigmoid function, Maltepe J. Math., 2 (2), (2020): 1121.
[19] Oyekan E.A., Lasode A.O. Estimates for some classes of analytic functions associated
with Pascal distribution series, error function, Bell numbers and q-dierential operator,
Nigerian J. Math. Appl., 32, (2022): 163173.
[20] Oyekan E.A., Swamy S.R., Opoola T.O. Ruscheweyh derivative and a new generalized
operator involving convolution, Internal. J. Math. Trends Technol., 67 (1) (2021): 88
100.
E.A. Oyekan, A.O. Lasode, T.A. Olatunji 67
[21] Oyekan E.A., Ojo O.O. Some properties of a class of analytic functions dened by
convolution of two generalized dierential operators, Intern. Confer. Contemp. Dev.
Math. Sci., 23, (2021): 724742.
[22] Oyekan E.A., Terwase A.J. Certain characterizations for a class of p-valent functions
dened by Salagean dierential operator, Gen. Math. Notes, 24 (2), (2014): 19.
[23] Ramachandran K., Dhanalakshmi C., Vanitha L. Hankel determinant for a subclass of
analytic functions associated with error functions bounded by conical regions, Internat.
J. Math. Anal., 11 (2), (2017): 571581.
[24] Thomas D.K., Tuneski N., Vasudevarao A. Univalent Functions: A Primer, Walter de
Gruyter Inc., Berlin, (2018)
