Sakaguchi type functions defined by balancing polynomials

Gunasekar Saravanan; Sudharsanan Baskaran; Balasubramaniam Vanithakumari; Serap Bulut

Mathematica Bohemica (2025)

  • Issue: 1, page 71-83
  • ISSN: 0862-7959

Abstract

top
The class of Sakaguchi type functions defined by balancing polynomials has been introduced as a novel subclass of bi-univalent functions. The bounds for the Fekete-Szegö inequality and the initial coefficients | a 2 | and | a 3 | have also been estimated.

How to cite

top

Saravanan, Gunasekar, et al. "Sakaguchi type functions defined by balancing polynomials." Mathematica Bohemica (2025): 71-83. <http://eudml.org/doc/299892>.

@article{Saravanan2025,
abstract = {The class of Sakaguchi type functions defined by balancing polynomials has been introduced as a novel subclass of bi-univalent functions. The bounds for the Fekete-Szegö inequality and the initial coefficients $\vert a_\{2\}\vert $ and $\vert a_\{3\}\vert $ have also been estimated.},
author = {Saravanan, Gunasekar, Baskaran, Sudharsanan, Vanithakumari, Balasubramaniam, Bulut, Serap},
journal = {Mathematica Bohemica},
keywords = {analytic function; bi-univalent function; Sakaguchi type function; balancing polynomial},
language = {eng},
number = {1},
pages = {71-83},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Sakaguchi type functions defined by balancing polynomials},
url = {http://eudml.org/doc/299892},
year = {2025},
}

TY - JOUR
AU - Saravanan, Gunasekar
AU - Baskaran, Sudharsanan
AU - Vanithakumari, Balasubramaniam
AU - Bulut, Serap
TI - Sakaguchi type functions defined by balancing polynomials
JO - Mathematica Bohemica
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 71
EP - 83
AB - The class of Sakaguchi type functions defined by balancing polynomials has been introduced as a novel subclass of bi-univalent functions. The bounds for the Fekete-Szegö inequality and the initial coefficients $\vert a_{2}\vert $ and $\vert a_{3}\vert $ have also been estimated.
LA - eng
KW - analytic function; bi-univalent function; Sakaguchi type function; balancing polynomial
UR - http://eudml.org/doc/299892
ER -

References

top
  1. Aktaş, İ., Karaman, İ., 10.55213/kmujens.1252471, KMU J. Eng. Natur. Sci. 5 (2023), 25-32. (2023) DOI10.55213/kmujens.1252471
  2. Aldawish, I., Al-Hawary, T., Frasin, B. A., 10.3390/math8050783, Mathematics 8 (2020), Article ID 783, 11 pages. (2020) MR4325637DOI10.3390/math8050783
  3. Amourah, A., Al-Hawary, T., Frasin, B. A., 10.1007/s13370-021-00881-x, Afr. Mat. 32 (2021), 1059-1066. (2021) Zbl1488.30030MR4293839DOI10.1007/s13370-021-00881-x
  4. Behera, A., Panda, G. K., 10.1080/00150517.1999.12428864, Fibonacci Q. 37 (1999), 98-105. (1999) Zbl0962.11014MR1690458DOI10.1080/00150517.1999.12428864
  5. Brannan, D. A., (eds.), J. G. Clunie, Aspects of Contemporary Complex Analysis, Academic Press, London (1980). (1980) Zbl0483.00007MR0623462
  6. Brannan, D. A., Clunie, J., Kirwan, W. E., 10.4153/CJM-1970-055-8, Can. J. Math. 22 (1970), 476-485. (1970) Zbl0197.35602MR0260994DOI10.4153/CJM-1970-055-8
  7. Davala, R. K., Panda, G. K., On sum and ratio formulas for balancing numbers, J. Indian Math. Soc., New Ser. 82 (2015), 23-32. (2015) Zbl1371.11038MR3290017
  8. Frasin, B. A., Coefficient inequalities for certain classes of Sakaguchi type functions, Int. J. Nonlinear Sci. 10 (2010), 206-211. (2010) Zbl1216.30008MR2745244
  9. Frontczak, R., 10.12988/ams.2018.87111, Appl. Math. Sci. 12 (2018), 1201-1208. (2018) DOI10.12988/ams.2018.87111
  10. Frontczak, R., 10.12988/ijma.2018.81067, Int. J. Math. Anal. 12 (2018), 585-594. (2018) DOI10.12988/ijma.2018.81067
  11. Frontczak, R., 10.12988/ams.2019.812183, Appl. Math. Sci. 13 (2019), 57-66. (2019) DOI10.12988/ams.2019.812183
  12. Keskin, R., Karaatlı, O., Some new properties of balancing numbers and square triangular numbers, J. Integer Seq. 15 (2012), Articl ID 12.1.4, 13 pages. (2012) Zbl1291.11030MR2872461
  13. Komatsu, T., Panda, G. K., On several kinds of sums of balancing numbers, Ars Comb. 153 (2020), 127-147. (2020) Zbl1513.11047MR4253120
  14. Lewin, M., 10.1090/S0002-9939-1967-0206255-1, Proc. Am. Math. Soc. 18 (1967), 63-68. (1967) Zbl0158.07802MR0206255DOI10.1090/S0002-9939-1967-0206255-1
  15. Netanyahu, E., 10.1007/BF00247676, Arch. Ration. Mech. Anal. 32 (1969), 100-112. (1969) Zbl0186.39703MR0235110DOI10.1007/BF00247676
  16. Owa, S., Sekine, T., Yamakawa, R., Notes on Sakaguchi functions, Aust. J. Math. Anal. Appl. 3 (2006), Article ID 12, 7 pages. (2006) Zbl1090.30024MR2223016
  17. Owa, S., Sekine, T., Yamakawa, R., 10.1016/j.amc.2006.08.133, Appl. Math. Comput. 187 (2007), 356-361. (2007) Zbl1113.30018MR2323589DOI10.1016/j.amc.2006.08.133
  18. Patel, B. K., Irmak, N., Ray, P. K., Incomplete balancing and Lucas-balancing numbers, Math. Rep., Buchar. 20 (2018), 59-72. (2018) Zbl1399.11045MR3781687
  19. Ray, P. K., Some congruences for balancing and Lucas-balancing numbers and their applications, Integers 14 (2014), Article ID A08, 8 pages. (2014) Zbl1284.11031MR3239589
  20. Ray, P. K., Balancing and Lucas-balancing sums by matrix methods, Math. Rep., Buchar. 17 (2015), 225-233. (2015) Zbl1374.11024MR3375730
  21. Ray, P. K., 10.1016/j.asej.2016.01.014, Ain Shams Engin. J. 9 (2018), 395-402. (2018) DOI10.1016/j.asej.2016.01.014
  22. Sakaguchi, K., 10.2969/jmsj/01110072, J. Math. Soc. Japan 11 (1959), 72-75. (1959) Zbl0085.29602MR0107005DOI10.2969/jmsj/01110072
  23. Shaba, T. G., Subclass of bi-univalent functions satisfying subordinate conditions defined by Frasin differential operator, Turkish J. Ineq. 4 (2020), 50-58. (2020) 
  24. Srivastava, H. M., Mishra, A. K., Gochhayat, P., 10.1016/j.aml.2010.05.009, Appl. Math. Lett. 23 (2010), 1188-1192. (2010) Zbl1201.30020MR2665593DOI10.1016/j.aml.2010.05.009
  25. Vijayalakshmi, S. P., Bulut, S., Sudharsan, T. V., 10.1142/S1793557122502126, Asian-Eur. J. Math. 15 (2022), Article ID 2250212, 9 pages. (2022) Zbl1504.30016MR4504278DOI10.1142/S1793557122502126
  26. Xu, Q.-H., Gui, Y.-C., Srivastava, H. M., 10.1016/j.aml.2011.11.013, Appl. Math. Lett. 25 (2012), 990-994. (2012) Zbl1244.30033MR2902367DOI10.1016/j.aml.2011.11.013
  27. Xu, Q.-H., Xiao, H.-G., Srivastava, H. M., 10.1016/j.amc.2012.05.034, Appl. Math. Comput. 218 (2012), 11461-11465. (2012) Zbl1284.30009MR2943990DOI10.1016/j.amc.2012.05.034
  28. Yousef, F., Amourah, A., Frasin, B. A., Bulboacă, T., 10.3390/axioms11060267, Axioms 11 (2022), Article ID 267, 8 pages. (2022) DOI10.3390/axioms11060267

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.