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.