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Year 2022, Volume: 10 Issue: 2, 368 - 374, 31.10.2022

Abstract

References

  • [1] R. M. Ali, S. K. Lee, V. Ravichandran and S. Supramaniam, Coefficient estimates for bi-univalent Ma-Minda stalike and convex functions, Appl. Math. Lett., 25(2012), no. 3, 344–351.
  • [2] M. K. Aouf, Bounded spiral-like functions with fixed second coefficient, Internat. J. Math. Math. Sci., 12(1989), no. 1, 113-118.
  • [3] M.K. Aouf, Bounded p􀀀valent Robertson functions of order a, Indian J. Pure Appl. Math., 16 (2001), no. 7, 775–790.
  • [4] M.K. Aouf and T.M. Seoudy, Certain class of bi–Bazilevic functions with bounded boundary rotation involving Salagean operator, Constructive Math. Anal., 3(2020), no. 4, 139–149.
  • [5] D. A. Brannan and T.S. Taha, D.A.Brannan,T.S.Taha,On some classes of bi-univalent functions, Studia Univ. Babe¸s-Bolyai Math.,31(1986), no. 2, 70–77.
  • [6] B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24(2011), no. 9, 1569–1573.
  • [7] S. P. Goyal and P. Goswami, Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, J. Egyptian Math. Soc., 20(2012), no.3, 179–182.
  • [8] P. K. Kulshrestha, Bounded Rebertson functions, Rend. Mat., 6 (1976), no. 7, 137–150.
  • [9] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18(1967), 63–68.
  • [10] R. J. Libera and A. E. Livingston, Bounded functions with postive real part, Czechoslovak Math. J., 22(1972), no. 97, 195-209.
  • [11] A. M. Nasr and M. K. Aouf, Bounded convex functions of complex order, Mansoura Sci. Bull., 10 (1983), 513–526.
  • [12] A. M. Nasr and M. K. Aouf, Bounded starlike functions of complex order, Proc. Indian Acad. Sci. (Math. Sci.), 92 (1983), no. 2, 97–102.
  • [13] M. S. Robertson, On the theory of univalent functions, Ann. Math., 37 (1936), 374–408.
  • [14] R. Singh and V. Singh, On a class of bounded starlike functions, Indian J. Pure Appl. Math., 5 (1974), 733–754.
  • [15] H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23(2010), 1188–1192.
  • [16] T. S. Taha, Topics in univalent function theory, Ph. D. Thesis, University of London,1981.

Classes of bi-Starlike and bi-Convex Bounded Functions with Complex Order

Year 2022, Volume: 10 Issue: 2, 368 - 374, 31.10.2022

Abstract

In this paper, estimates for second and third coefficients of certain classes of bi-starlike and bi-convex bounded functions with complex order in the open unit disk are determined, and certain special cases are also indicated.

References

  • [1] R. M. Ali, S. K. Lee, V. Ravichandran and S. Supramaniam, Coefficient estimates for bi-univalent Ma-Minda stalike and convex functions, Appl. Math. Lett., 25(2012), no. 3, 344–351.
  • [2] M. K. Aouf, Bounded spiral-like functions with fixed second coefficient, Internat. J. Math. Math. Sci., 12(1989), no. 1, 113-118.
  • [3] M.K. Aouf, Bounded p􀀀valent Robertson functions of order a, Indian J. Pure Appl. Math., 16 (2001), no. 7, 775–790.
  • [4] M.K. Aouf and T.M. Seoudy, Certain class of bi–Bazilevic functions with bounded boundary rotation involving Salagean operator, Constructive Math. Anal., 3(2020), no. 4, 139–149.
  • [5] D. A. Brannan and T.S. Taha, D.A.Brannan,T.S.Taha,On some classes of bi-univalent functions, Studia Univ. Babe¸s-Bolyai Math.,31(1986), no. 2, 70–77.
  • [6] B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24(2011), no. 9, 1569–1573.
  • [7] S. P. Goyal and P. Goswami, Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, J. Egyptian Math. Soc., 20(2012), no.3, 179–182.
  • [8] P. K. Kulshrestha, Bounded Rebertson functions, Rend. Mat., 6 (1976), no. 7, 137–150.
  • [9] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18(1967), 63–68.
  • [10] R. J. Libera and A. E. Livingston, Bounded functions with postive real part, Czechoslovak Math. J., 22(1972), no. 97, 195-209.
  • [11] A. M. Nasr and M. K. Aouf, Bounded convex functions of complex order, Mansoura Sci. Bull., 10 (1983), 513–526.
  • [12] A. M. Nasr and M. K. Aouf, Bounded starlike functions of complex order, Proc. Indian Acad. Sci. (Math. Sci.), 92 (1983), no. 2, 97–102.
  • [13] M. S. Robertson, On the theory of univalent functions, Ann. Math., 37 (1936), 374–408.
  • [14] R. Singh and V. Singh, On a class of bounded starlike functions, Indian J. Pure Appl. Math., 5 (1974), 733–754.
  • [15] H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23(2010), 1188–1192.
  • [16] T. S. Taha, Topics in univalent function theory, Ph. D. Thesis, University of London,1981.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mohamed Kamal Aouf

Tamer Seoudy

Publication Date October 31, 2022
Submission Date February 22, 2021
Acceptance Date August 10, 2022
Published in Issue Year 2022 Volume: 10 Issue: 2

Cite

APA Aouf, M. K., & Seoudy, T. (2022). Classes of bi-Starlike and bi-Convex Bounded Functions with Complex Order. Konuralp Journal of Mathematics, 10(2), 368-374.
AMA Aouf MK, Seoudy T. Classes of bi-Starlike and bi-Convex Bounded Functions with Complex Order. Konuralp J. Math. October 2022;10(2):368-374.
Chicago Aouf, Mohamed Kamal, and Tamer Seoudy. “Classes of Bi-Starlike and Bi-Convex Bounded Functions With Complex Order”. Konuralp Journal of Mathematics 10, no. 2 (October 2022): 368-74.
EndNote Aouf MK, Seoudy T (October 1, 2022) Classes of bi-Starlike and bi-Convex Bounded Functions with Complex Order. Konuralp Journal of Mathematics 10 2 368–374.
IEEE M. K. Aouf and T. Seoudy, “Classes of bi-Starlike and bi-Convex Bounded Functions with Complex Order”, Konuralp J. Math., vol. 10, no. 2, pp. 368–374, 2022.
ISNAD Aouf, Mohamed Kamal - Seoudy, Tamer. “Classes of Bi-Starlike and Bi-Convex Bounded Functions With Complex Order”. Konuralp Journal of Mathematics 10/2 (October 2022), 368-374.
JAMA Aouf MK, Seoudy T. Classes of bi-Starlike and bi-Convex Bounded Functions with Complex Order. Konuralp J. Math. 2022;10:368–374.
MLA Aouf, Mohamed Kamal and Tamer Seoudy. “Classes of Bi-Starlike and Bi-Convex Bounded Functions With Complex Order”. Konuralp Journal of Mathematics, vol. 10, no. 2, 2022, pp. 368-74.
Vancouver Aouf MK, Seoudy T. Classes of bi-Starlike and bi-Convex Bounded Functions with Complex Order. Konuralp J. Math. 2022;10(2):368-74.
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