Sandwich theorems for a class of p-valent meromorphic functions involving the Erdélyi–Kober-type integral operators

Sandwich theorems for a class of p-valent meromorphic functions involving the Erdélyi–Kober-type integral operators

In this paper, the authors study some subordination and superordination properties for classes of p-valentmeromorphic, analytic, and univalent functions associated with a linear operator $Lm,ℓp,λ (a, c, µ)$ of the Erdélyi–Kober type. Connections with several earlier results are also pointed out.

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  • Ali RM, Ravichandran V, Seenivasagan N. Subordination and superordination on Schwarzian derivatives. J Inequal Appl 2008; Art. ID 712328: 1-18.
  • Ali RM, Ravichandran V, Seenivasagan N. Differential subordination and superordination of analytic functions defined by the multiplier transformation. Math Inequal Appl 2009; 12: 123-139.
  • Aouf MK. New criteria for multivalent meromorphic starlike functions of order alpha. Proc Japan Acad Ser A Math Sci 1993; 69: 66-70.
  • Aouf MK, Shamandy A, Mostafa AO, El-Emam FZ. On certain subclasses of meromorphically p-valent functions associated with integral operators. European J Pure Appl Math 2011; 4: 435-447.
  • Aouf MK, Srivastava HM. A new criterion for meromorphically p-valent convex functions of order alpha. Math Sci Res Hot-Line 1997; 8: 7-12.
  • Al-Oboudi FM, Al-Zkeri HA. Applications of Briot-Bouquet differential subordination to certain classes of meromorphic functions. Arab J Math Sci 2005; 12: 1-14.
  • Aqlan E, Jahangiri JM, Kulkarni SR. Certain integral operators applied to meromorphic p-valent functions. J Natur Geom 2003; 24: 111-120.
  • Bulboacă T. Integral operators that preserve the subordination. Bull Korean Math Soc 1997; 34: 627-636.
  • Cho NE, Bulboacă T, Srivastava HM. A general family of integral operators and associated subordination and superordination properties of some special analytic function classes. Appl Math Comput 2012; 219: 2278-2288.
  • Cho NE, Known OS, Srivastava HM. Inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations. J Math Anal Appl 2004; 300: 505-520.
  • Cho NE, Known OS, Srivastava HM. Inclusion relationships for certain subclasses of meromorphic functions associated with a family of multiplier transformations. Integral Transforms Spec Funct 2005; 16: 647-659.
  • Cho NE, Owa S. Double subordination preserving properties for certain integral operators. J Inequal Appl 2007; Art. ID 83073: 1-10.
  • Cho NE, Srivastava HM. A class of non-linear integral operators preserving subordination and superordination. Integral Transforms Spec Funct 2007; 18: 95-107.
  • Duren PL. Univalent Functions. New York, NY, USA: Springer-Verlag, 1983.
  • El-Ashwah RM. A note on certain meromorphic p-valent functions. Appl Math Lett 2009; 22: 1756-1759.
  • El-Ashwah RM. Properties of certain class of p-valent meromorphic functions associated with new integral operator. Acta Univ Apulensis Math Inform No 2012; 9: 255-264.
  • El-Ashwah RM. Certain class of meromorphic univalent functions defined by an Erdélyi-Kober type integral operator. Open Sci J Math Appl 2015; 3: 7-13.
  • El-Ashwah RM, Aouf MK, Abd-Eltawab AM. On certain classes of p-valent meromorphic functions associated with a family of integral operators. European J Math Sci 2013; 2: 85-90.
  • El-Ashwah RM, Drbuk ME. Subordination properties of p-valent functions defined by linear operators. British Journal of Mathematics & Computer Science 2014; 4: 3000-3013.
  • El-Ashwah RM, Hassan AH. Some inequalities of certain subclass of meromorphic functions defined by using new integral operator. Inform Sci Comput 2014; 3: 1-10.
  • Gronwall TH. Some remarks on conformal representation. Ann Math 1914; 16: 72-76.
  • Kumar V, Shukla SL. Certain integrals for classes of p-valent meromorphic functions. Bull Austral Math Soc 1982; 25: 85-97.
  • Lashin AY. On certain subclass of meromorphic functions associated with certain integral operators. Comput Math Appl 2010; 59: 524-531.
  • Liu JL, Srivastava HM. A linear operator and associated families of meromorphically multivalent functions. J Math Anal Appl 2001; 259: 566-581.
  • Miller SS, Mocanu PT. Differential subordinations and univalent functions. Michigan Math J 1981; 28: 157-171.
  • Miller SS, Mocanu PT. Univalent solutions of Briot-Bouquet differential equations. J Differential Equations 1985; 56: 297-309.
  • Miller SS, Mocanu PT. Differential Subordinations : Theory and Applications. New York, NY, USA: Marcel Dekker Incorporated, 2000.
  • Miller SS, Mocanu PT. Subordinants of differential superordinations. Complex Variables Theory Appl 2003; 48: 815-826.
  • Miller SS, Mocanu PT, Reade MO. Subordination-preserving integral operators. Trans Amer Math Soc 1984; 283: 605-615.
  • Pommerenke CH. Univalent Functions. Göttingen, Germany: Vanderhoeck and Ruprecht, 1975.
  • Raina RK, Sharma P. Subordination preserving properties associated with a class of operators. Matematiche (Catania) 2013; 68: 217-228.
  • Shanmugam TN, Sivasubramanian S, Srivastava HM. Differential sandwich theorems for certain subclasses of analytic functions involving multiplier transformations. Integral Transforms Spec Funct 2006; 17: 889-899.
  • Srivastava HM, Aouf MK, Mostafa AO, Zayed HM. Certain subordination-preserving family of integral operators associated with p-valent functions. Appl Math Inform Sci 2017; 11: 951-960.
  • Uralegaddi BA, Somanatha C. New criteria for meromorphic starlike univalent functions. Bull Austral Math Soc 1991; 43: 137-140.
  • Uralegaddi BA, Somanatha C. Certain classes of meromorphic multivalent functions. Tamkang Journal of Mathematics 1992; 23: 223-231.
  • Wang ZG, Xiang RG, Darus M. A family of integral operators preserving subordination and superordination. Bull Malays Math Sci Soc 2010; 33: 121-131.