Saray, N., Juma, A. (2025). FEKETE-SZEGÖ INEQUALITIES FOR QUASI-SUBORDINATION FUNCTION USING NEW SUBCLASS. , 1(1), 1-6. doi: 10.63298/asj.2025.184946
Noor F. Saray; Abdul Rahman S. Juma. "FEKETE-SZEGÖ INEQUALITIES FOR QUASI-SUBORDINATION FUNCTION USING NEW SUBCLASS". , 1, 1, 2025, 1-6. doi: 10.63298/asj.2025.184946
Saray, N., Juma, A. (2025). 'FEKETE-SZEGÖ INEQUALITIES FOR QUASI-SUBORDINATION FUNCTION USING NEW SUBCLASS', , 1(1), pp. 1-6. doi: 10.63298/asj.2025.184946
Saray, N., Juma, A. FEKETE-SZEGÖ INEQUALITIES FOR QUASI-SUBORDINATION FUNCTION USING NEW SUBCLASS. , 2025; 1(1): 1-6. doi: 10.63298/asj.2025.184946

FEKETE-SZEGÖ INEQUALITIES FOR QUASI-SUBORDINATION FUNCTION USING NEW SUBCLASS

Anbar Science Journal
Volume 1, Issue 1, February 2025, Pages 1-6    PDF (487.24 K)
Document Type: Original Article
DOI: 10.63298/asj.2025.184946
Authors
Noor F. Saray; Abdul Rahman S. Juma*
Department of Mathematics, College of Education for Pure Sciences, University of Anbar, Iraq
Abstract
This study focuses on deriving Fekete-Szegö inequalities for a specific subclass of univalent functions with complex order, related to quasi-subordination. It investigates the geometric properties of these functions and the conditions for subordination between analytic functions within the open unit disk. The research also discusses generalized starlikeness and convexity as examples of subordination and explores the role of analytic Schwarz functions in this context. New results are provided for superior functions of various orders, contributing to the field of geometric function theory. The findings offer insights into quasi-subordination and its practical applications in pure mathematics, advancing the understanding of function behavior under subordination constraints.

Highlights
  • Investigates Fekete-Szegö inequalities for a specific subclass of univalent functions.
  • Explores quasi-subordination and its implications in geometric function theory.
  • Analyzes geometric properties of analytic functions within the open unit disk.
  • Introduces new conditions for subordination, majorization, and function constraints.
  • Provides novel results on superior functions of various orders, contributing to pure mathematics.
Keywords
Fekete-Szegö inequality; Quasi-subordination; Majorization; Holomorphic functions
References
  • Al-Shaqsi and M. Darus, On Fekete-Szego¨ Problems for Certain Subclass of Analytic Functions, Applied Mathematical Sciences, 2(9)(2008), 431–441.
  • Altintas and Sh. Owa, Majorizations and quasi-subordinations for certain analytic functions, Proc. Japan Acad. Ser. A Math. Sci., 68(7)(1992), 181–185.
  • H. Shehab and A. R. S. Juma, Third Order Differential Subordination for Analytic Functions Involving Convolution Operator. Baghdad Science Journal, 19(3) (2022), 0581-0581
  • L. Duren, ’Univalent functions’, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.
  • Fekete and G. Szeg¨o, Eine bemerkung uberungerade schlichte funktionen, J. Lond. Math. Soc., 8(1933), 85–89.
  • Goswami and M. K. Aouf, Majorization properties for certain classes of analytic functions using the Scalcagean operator, Appl. Math. Lett., 23(11)(2010), 1351–1354.
  • Hashidume and Sh. Owa, Majorization problems for certain analytic functions, Int. J. Open Problems Compt. Math., 1(3)(2008), 179–187.
  • Kanas, An unified approach to the Fekete-Szego¨ problem, Appl. Math. Comput., 218(2012), 8453–8461.
  • [S. Kanas, Differential subordination related to conic sections, J. Math. Anal. Appl., 317(2)(2006), 650–658.
  • Kanas, Subordinations for domains bounded by conic sections, Bull. Belg. Math. Soc. Simon Stevin, 15(2008), 1–10.
  • Kanas, Techniques of the differential subordination for domains bounded by conic sections, Int. J. Math. Math. Sci., 38(2003), 2389–2400.
  • Kanas, O. Crisan, Differential subordinations involving arithmetic and geometric means, Appl. Math. Comput., 222(2013), 123–131.
  • Kanas and H. E. Darwish, Fekete-Szego¨ problem for starlike and convex functions of complex order, Appl. Math. Letters, 23(2010), 777–782.
  • R. Keogh and E. P. Merkes, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., 20(1969), 8–12.
  • H. Shehab and A. R. S. Juma, "Quasi subordination of bi-univalent functions involving convolution operator," in AIP Conference Proceedings, 2022, vol. 2398, no. 1: AIP Publishing LLC, p. 060062.
  • H. MacGregor, Majorization by univalent functions, Duke Math. J., 34(1967), 95–102.
  • Ma and D. Minda, A unified treatment of some special classes of univalent functions, in Proceedings of the conference on complex Analysis, Z. Li, F. Ren, L. Lang and S. Zhang (Eds.), Int. Press (1994), 157-169.
  • S. Miller and P. T. Mocanu, Differential subordinations: Theory and Applications, Marcel Dekker, Inc., New York, 2000.
  • H. Shehab and A. R. S. Juma, "Application of Quasi Subordination Associated with Generalized Sakaguchi Type Functions," Iraqi Journal of Science, pp. 4885-4891, 2021.
  • Murugusundaramoorthy, S. Kavitha and T. Rosy, On the Fekete-Szego¨ problem for some subclasses of analytic functions defined by convolution, Proc. Pakistan Acad. Sci., 44(2007), 249–254.
  • S. Robertson, Quasi-subordination and coefficient conjectures, Bull. Amer. Math. Soc., 76(1970), 1–9.
  • N. Shanmugam and S. Sivasubramanian, On the Fekete-Szego¨ problem for some subclasses of analytic functions, J. Inequal. Pure Appl. Math., 6(3)(2005), 1–15.
  • M. Srivastava, A. K. Mishra and M. K. Das, The Fekete-Szeg¨o problem for a subclass of close-to-convex functions, Complex Variables Theory Appl., 44(2001), 145–163. 
Statistics
Article View: 1,196
PDF Download: 153


Journal Management System. Powered by iJournalPro.com