Initial bounds for analytic function classes characterized by certain special functions and bell numbers

Authors

DOI:

https://doi.org/10.26577/JMMCS2023v120i4a5
        222 70

Keywords:

Analytic function, Schwarz function, (p-q) Chebyshev polynomial, (p-q) Gegenbauer polynomial, coefficient estimate, Fekete-Szego problem, subordination

Abstract

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

Abramowitz M., Stegun I.A. (eds.). Handbook of Mathematical Functions with Formulas,

Graphs and Mathematical Tables, Dover Publications Inc., New York, (1965).

Aral A., Gupta V., Agarwal R.P. Applications of q-Calculus in Operator Theory, Springer

Science+Business Media, New York, (2013).

Bell E.T. Exponential polynomials, Ann. Math., 35, (1934): 258277.

Bell E.T. The iterated exponential integers, Ann. Math., 39, (1938): 539557.

Coman D. The radius of starlikeness for error function, Stud. Univ. Babes Bolyal Math.,

, (1991): 1316.

Initial bounds for analytic function classes characterized by certain special functions . . .

Elbert A., Laforgia A. The zeros of the complementary error function, Numer.

Algorithms, 49 (1-4), (2008): 153157.

Jackson F.H. On q-functions and a certain dierence operator, Trans. Roy. Soc. Edinb.,

(2), (1908): 6472.

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.

Kac V., Cheung P., Quantum Calculus, Springer-Verlag Inc., New York, (2002).

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.

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.

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.

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.

Nisar K.S., Baleanu D., Qurashi M.A. Fractional calculus and application of generalized

Struve function, SpringerPlus J., 5 (910), (2016): 13 pages.

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).

Oyekan E.A. Coecient estimates and subordination results for certain classes of

analytic functions, J. Math. Sci., 24 (2), (2013): 7586.

Oyekan E.A. Certain geometric properties of functions involving Galue type Struve

function, Ann. Math. Comput. Sci., 8, (2022): 4353.

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.

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.

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

E.A. Oyekan, A.O. Lasode, T.A. Olatunji 67

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.

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.

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.

Thomas D.K., Tuneski N., Vasudevarao A. Univalent Functions: A Primer, Walter de

Gruyter Inc., Berlin, (2018)

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2023-12-31 — Updated on 2024-03-29

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How to Cite

Oyekan, E., Lasode, A., & Olatunji, T. (2024). Initial bounds for analytic function classes characterized by certain special functions and bell numbers. Journal of Mathematics, Mechanics and Computer Science, 120(4), 41–51. https://doi.org/10.26577/JMMCS2023v120i4a5 (Original work published December 31, 2023)