### A Study of Meromorphically Univalent Functions Defined by a Linear Operator Associated with the $\lambda$-Generalized Hurwitz-Lerch Zeta Function

#### Abstract

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#### References

S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc.,

(1969), 429{446.

B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions,

SIAM J. Math. Anal., 15 (1984), 737{745.

N. E. Cho, I. H. Kim and H. M. Srivastava, Sandwich-type theorems for multivalent

functions associated with the Srivastava-Attiya operator, Appl. Math. Comput., 217

(2010), 918{928.

N. E. Cho and H. M. Srivastava, Argument estimation of certain analytic functions

dened by a class of multiplier transformation, Math. Comput. Modelling, 37 (2003),

{49.

J. H. Choi, M. Saigo and H. M. Srivastava, Some inclusion properties of a certain

family of integral operators, J. Math. Anal. Appl., 276 (2002), 432{445.

J. Dziok and H. M. Srivastava, Classes of analytic functions associated with the gen-

eralized hypergeometric function, Appl. Math. Comput., 103 (1999), 1{13.

J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated

with the generalized hypergeometric function, Integral Transforms Spec. Funct., 14

(2003), 7{18.

F. Ghanim, A study of a certain subclass of Hurwitz-Lerch zeta function related to a

linear operator, Abstr. Appl. Anal., 2013 Article ID 763756 (2013), 1{7.

F. Ghanim and M. Darus, New result of analytic functions related to Hurwitz-Zeta

function, The Scientic World Journal, vol. 2013, Article ID 475643, 5 pages, 2013.

doi:10.1155/2013/475643.

D. I. Hallenbeck and S. Ruscheweyh, Subordination by convex functions, Proc. Amer.

Math. Soc., 52 (1975), 191{195.

Yu. E. Hohlov, Operators and operations in the class of univalent functions, Izv. Vyss.

Ucebn. Zaved. Matematika, 10 (1978), 83{89.

V. Kiryakova, Criteria for univalence of the Dziok-Srivastava and the Srivastava-Owa

operators in the class A, Appl. Math. Comput., 218 (2011), 883{892.

I. B. Jung, Y. C. Kim and H. M. Srivastava, The Hardy space of analytic functions

associated with certain one-parameter families of integral operators, J. Math. Anal.

Appl., 176 (1993), 138{147.

A. M. Mathai, R. K. Saxena and H. J. Haubold, The H-Function: Theory and Appli-

cations, Springer, New York, Dordrecht, Heidelberg and London, 2010.

K. I. Noor and S. Z. H. Bukhari, Some subclasses of analytic and spiral-like functions

of complex order involving the Srivastava-Attiya integral operator, Integral Transforms

Spec. Funct., 21 (2010), 907{916.

S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric func-

tions, Canad. J. Math., 39 (1987), 1057{1077.

S.S. Miller and P.T. Mocanu, Differential subordinations: theory and applications,

Series in Pure and Applied Mathematics, 225, Marcel Dekker, New York, (2000).

S. Owa, M. Nunokawa, H. Saitoh and H.M. Srivastava, Close-to-convexity, starlike-

ness, and convexity of certain analytic functions, Appl. Math. Lett., 15 (1)(2002),

-69.

J. K. Prajapat and T. Bulboaca, Double subordination preserving properties for a

new generalized Srivastava-Attiya operator, Chin. Ann. Math., 33 (2012), 569{582.

D. Raducanu and H. M. Srivastava, A new class of analytic functions dened by

means of a convolution operator involving the Hurwitz-Lerch zeta function, Integral

Transforms Spec. Funct., 18 (2007), 933{943.

S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc., 49,

(1975), 109{115.

H. M. Srivastava, Some Fox-Wright generalized hypergeometric functions and as-

sociated families of convolution operators, Appl. Anal. Discrete Math., 1 (2007),

{71.

H. M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational

arguments, Math. Proc. Cambridge Philos. Soc., 129, (2000), 77{84.

H. M. Srivastava, Some generalizations and basic (or q-) extensions of the Bernoulli,

Euler and Genocchi polynomials, Appl. Math. Inform. Sci., 5 (2011), 390{444.

H. M. Srivastava, Generating relations and other results associated with some families

of the extended Hurwitz-Lerch Zeta functions, SpringerPlus, 2 (2013), Article ID 2:

, 1{14.

H. M. Srivastava, A new family of the -generalized Hurwitz-Lerch zeta functions with

applications, Appl. Math. Inform. Sci., 8(2014), 1485{1500.

H. M. Srivastava and A. A. Attiya, An integral operator associated with the Hurwitz-

Lerch zeta function and differential subordination, Integral Transforms Spec. Funct.,

, (2007), 207{216.

H. M. Srivastava and J. Choi, Series Associated with Zeta and Related Functions,

Kluwer Academic Publishers, Dordrecht, Boston and London, 2001.

H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and

Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.

H. M. Srivastava and S. Gaboury, New expansion formulas for a family of the -

generalized Hurwitz-Lerch zeta functions, Internat. J. Math. Math. Sci., 2014 (2014),

Article ID 131067, 1{13.

H. M. Srivastava and S. Gaboury, A new class of analytic functions dened by means

of a generalization of the Srivastava-Attiya operator, J. Inequal. Appl., 25 (2015),

Article ID 39, 1{15.

H. M. Srivastava, S. Gaboury and A. Bayad, Expansion formulas for an extended

Hurwitz-Lerch zeta function obtained via fractional calculus, Adv. Difference Equa-

tions, 2014 (2014), Article ID 169, 1{17.

H. M. Srivastava, S. Gaboury and B.-J. Fugere, Further results involving a class of

generalized Hurwitz-Lerch zeta functions, Russian J. Math. Phys., 21, (2014), 521-

H. M. Srivastava, S. Gaboury and F. Ghanim, Certain subclasses of meromorphi-

cally univalent functions dened by a linear operator associated with the -generalized

Hurwitz-Lerch zeta function, Integral Transforms Spec. Funct., 26 (4), (2015), 258{

H. M. Srivastava, S. Gaboury and F. Ghanim, Some Further Properties of a Linear

Operator Associated with the -Generalized Hurwitz-Lerch Zeta Function Related to

the Class of Meromorphically Univalent Functions, Applied Mathematics and Com-

putation, 259, (2015), 1019-1029.

H. M. Srivastava, S. Gaboury and R. Tremblay, New relations involving an extended

multiparameter Hurwitz-Lerch zeta function with applications, Int. J. Anal., 2014

(2014), Article ID 680850, 1{21.

H. M. Srivastava, K. C. Gupta and S. P. Goyal, The H-Functions of One and Two

Variables with Applications, South Asian Publishers, New Delhi, New Delhi and

Madras, 1982.

H. M. Srivastava, D. Jankov, T. K. Pogany and R. K. Saxena, Two-sided inequalities

for the extended Hurwitz-Lerch Zeta function, Comput. Math. Appl., 62 (2011),

{522.

H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted

Press (Ellis Horwoord Limited, Chichester), John Wiley and Sons, New York, Chich-

ester, Brisbane and Toronto, 1984.

H. M. Srivastava, D. Raducanu and G. S. Salagean, A new class of generalized close-

to-starlike functions dened by the Srivastava-Attiya operator, Acta Math. Sinica

(English Ser.) 29 (2013), 833{840.

H. M. Srivastava, R. K. Saxena, T. K. Pogany and R. Saxena, Integral and compu-

tational representations of the extended Hurwitz-Lerch zeta function, Integral Trans-

forms Spec. Funct., 22 (2011), 487{506.

Z.-G. Wang, H. M. Srivastava and S.-M. Yuan, Some basic properties of certain

subclasses of meromorphically starlike functions, J. Inequal. Appl. 2014 (2014),

Article ID 2014:29, 1{12.

S.-M. Yuan, Z.-M. Liu and H. M. Srivastava, Some inclusion relationships and

integral-preserving properties of certain subclasses of meromorphic functions asso-

ciated with a family of integral operators, J. Math. Anal. Appl., 337 (2008), 505-515.

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