Double subordination preserving properties for a new generalized Srivastava-Attiya integral operator

Jugal K. Prajapat , Teodor Bulboacă

Chinese Annals of Mathematics, Series B ›› 2012, Vol. 33 ›› Issue (4) : 569 -582.

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Chinese Annals of Mathematics, Series B ›› 2012, Vol. 33 ›› Issue (4) : 569 -582. DOI: 10.1007/s11401-012-0722-3
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Double subordination preserving properties for a new generalized Srivastava-Attiya integral operator

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Abstract

The authors obtain subordination and superordination preserving properties for a new defined generalized operator involving the Srivastava-Attiya integral operator. Differential sandwich-type theorems for these univalent functions, and some consequences involving well-known special functions are also presented.

Keywords

Differential subordination and superordination / Analytic functions, Univalent functions / Starlike functions / Convex functions / Srivastava-Attiya integral operator / Hypergeometric functions

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Jugal K. Prajapat, Teodor Bulboacă. Double subordination preserving properties for a new generalized Srivastava-Attiya integral operator. Chinese Annals of Mathematics, Series B, 2012, 33(4): 569-582 DOI:10.1007/s11401-012-0722-3

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References

[1]

Ali R. M., Ravichandran V., Seenivasagan N.. Subordination and superordination of the Liu-Srivastava linear operator on meromorphic functions. Bull. Malays. Math. Sci. Soc., 2008, 31(2): 192-207

[2]

Ali R. M., Ravichandran V., Seenivasagan N.. Differential subordination and superordination of analytic functions defined by the multiplier transformation. Math. Inequal. Appl., 2009, 12: 123-139

[3]

Bernardi S. D.. Convex and starlike univalent functions. Trans. Amer. Math. Soc., 1969, 135: 429-446

[4]

Bulboacă T.. Integral operators that preserve the subordination. Bull. Korean Math. Soc., 1997, 34: 627-636

[5]

Bulboacă T.. A class of superordination-preserving integral operators. Indag. Math. (N. S.), 2002, 13: 301-311

[6]

Carlson B. C., Shaffer D. B.. Starlike and prestarlike hypergeometric functions. SIAM J. Math. Anal., 1984, 15: 737-745

[7]

Cho N. E., Srivastava H. M.. Argument estimation of certain analytic functions defined by a class of multiplier transformation. Math. Comput. Modelling, 2003, 37: 39-49

[8]

Choi J. H., Saigo M., Srivastava H. M.. Some inclusion properties of a certain family of integral operators. J. Math. Anal. Appl., 2002, 276: 432-445

[9]

Garg M., Jain K., Kalla S. L.. On generalized Hurwitz-Lerch Zeta distribution. Appl. Appl. Math., 2009, 4: 26-39

[10]

Goyal S. P., Laddha R. K.. On generalized Riemann zeta function and generalized Lambert’s transform. Gan. ita Sandesh, 1997, 11: 99-108

[11]

Goyal S. P., Prajapat J. K.. Certain formulas for unified Riemann Zeta and related functions. J. Rajasthan Acad. Phys. Sci., 2004, 3(4): 267-274

[12]

Gronwall T. H.. Some remarks on conformal representation. Ann. Math., 1914, 16: 72-76

[13]

Jung I. B., Kim Y. C., Srivastava H. M.. The Hardy space of analytic functions associated with certain one-parameter families of integral operators. J. Math. Anal. Appl., 1993, 176: 138-147

[14]

Miller S. S., Mocanu P. T.. Second order differential inequalities in the complex plane. J. Math. Anal. Appl., 1978, 65: 289-305

[15]

Miller S. S., Mocanu P. T.. Differential subordinations and univalent functions. Michigan Math. J., 1981, 28: 157-171

[16]

Miller S. S., Mocanu P. T.. Differential Subordinations, Theory and Applications, 2000, New York, Basel: Marcel Dekker

[17]

Miller S. S., Mocanu P. T.. Subordinants of differential superordinations. Comp. Var. Theory Appl., 2003, 48: 815-826

[18]

Miller S. S., Mocanu P. T., Reade M. O.. Subordination-preserving integral operators. Trans. Amer. Math. Soc., 1984, 283: 605-615

[19]

Noor K. I., Bukhari S. Z. H.. Some subclasses of analytic and spiral-like functions of complex order involving the Srivastava-Attiya integral operator. Integral Transforms Spec. Funct., 2010, 21(12): 907-916

[20]

Owa S., Srivastava H. M.. Univalent and starlike generalized hypergeometric functions. Canad. J. Math., 1987, 39: 1057-1077

[21]

Pommerenke C.. Univalent Functions, 1975, Göttingen: Vanderhoeck and Ruprecht

[22]

Prajapat J. K., Goyal S. P.. Application of Srivastava-Attiya operator to the classes of strongly starlike and strongly convex functions. J. Math. Inequal., 2009, 3: 129-137

[23]

Prajapat J. K., Raina R. K.. New sufficient conditions for starlikeness of analytic functions involving a fractional differ-integral operator. Demonstratio Math., 2010, 18(4): 805-813

[24]

Srivastava H. M., Attiya A. A.. An integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination. Integral Transforms Spec. Funct., 2007, 18(3): 207-216

[25]

Srivastava H. M., Choi J.. Series Associated with the Zeta and Related Functions, 2001, Dordrecht, Boston, London: Kluwer Academic Publishers

[26]

Srivastava H. M., Saxena R. K., Pogany T. K. Integral and computational representations of the extended Hurwitz-Lerch Zeta function. Integral Transforms Spec. Funct., 2011, 22(7): 487-506

[27]

Xiang R. G., Wang Z. G., Darus M.. A family of integral operators preserving subordination and superordination. Bull. Malays. Math. Sci. Soc. (2), 2010, 33(1): 121-131

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