Advertisement

Study of Analytic Functions Related with Simply Connected Convex Set

  • M. I. FaisalEmail author
Research Paper
  • 11 Downloads
Part of the following topical collections:
  1. Mathematics

Abstract

In this paper, making use of a linear differential operator we introduce and study a new class of a simply connected convex set of meromorphic functions. We obtain some inclusion outcomes and their geometric properties.

Keywords

Analytic functions Differential operator Meromorphic convex functions Open unit disk 

Mathematics Subject Classification

Primary 30C45 

Notes

Acknowledgements

The author is deeply grateful to the conciliators for giving productive criticisms and helps in updating the content of this study.

References

  1. Aouf MK, Hossen HM (1993) New criteria for meromorphic \(p\)-valent starlike functions. Tsukuba J Math 17:481–486MathSciNetCrossRefzbMATHGoogle Scholar
  2. Aouf MK, El-Ashwah RM, Zayed HM (2014) Fekete–Szego inequalities for \(p\)-valent starlike and convex functions of complex order. J Egypt Math Soc 22:190–196MathSciNetCrossRefzbMATHGoogle Scholar
  3. El-Ashwah RM, Hassan AH (2016) Properties of certain subclass of p-valent meromorphic functions associated with certain linear operator. J Egypt Math Soc 24:226–232MathSciNetCrossRefzbMATHGoogle Scholar
  4. Gundersen GG (2017) Research questions on meromorphic functions and complex differential equations. Comput Methods Funct Theory 17:195–209MathSciNetCrossRefzbMATHGoogle Scholar
  5. Liu J-L, Srivastava HM (2004a) Classes of meromorphically multivalent functions associated with the generalized hypergeometric function. Comput Methods Funct Theory 39:21–34MathSciNetzbMATHGoogle Scholar
  6. Liu JL, Srivastava HM (2004b) Classes of meromorphically multivalent functions associated with the generalized hypergeometric function. Math Comput Model 39:21–34MathSciNetCrossRefzbMATHGoogle Scholar
  7. Miller SS (1975) Differential inequalities and Caratheodory functions. Bull Am Math Soc 81:79–81MathSciNetCrossRefzbMATHGoogle Scholar
  8. Miller SS, Mocanu PT (1978) Second order differential inequalities in the complex plane. J Math Anal Appl 65:289–305MathSciNetCrossRefzbMATHGoogle Scholar
  9. Noor KI (2006) On certain classes of analytic functions. J Inequal Pure Appl Math 7:1–5MathSciNetGoogle Scholar
  10. Padmanabhan KS, Parvatham R (1975) Properties of a class of functions with bounded boundary rotation. Ann Polon Math 31:311–323MathSciNetCrossRefzbMATHGoogle Scholar
  11. Piejko K, Sokol J (2008) Subclasses of meromorphic functions associated with the Cho–Kwon–Srivastava operator. J Math Anal Appl 337:1261–1266MathSciNetCrossRefzbMATHGoogle Scholar
  12. Pinchuk B (1971) Functions with bounded boundary rotation. Isr J Math 10:7–16MathSciNetCrossRefzbMATHGoogle Scholar
  13. Qi J, Meng F, Yuan W (2018) Normal families and growth of meromorphic functions with their \(K\)th derivatives. J Funct Spaces 2018:1–8CrossRefGoogle Scholar
  14. Raina RK, Sharma P (2012) On a class of meromorphic functions defined by a composition structure of two linear operators. Adv. Stud. Contemp. Math. 22:565–578MathSciNetzbMATHGoogle Scholar
  15. Uralegaddi BA, Somanatha C (1991) New criteria for meromorphic starlike univalent functions. Bull Austral Math Soc 43:137–140MathSciNetCrossRefzbMATHGoogle Scholar
  16. Wang ZG, Sunc Y, Zhang ZH (2009) Certain classes of meromorphic multivalent functions. Comput Math Appl 58:1408–1417MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Department of MathematicsTaibah UniversityMedinaKingdom of Saudi Arabia

Personalised recommendations