### RADIUS CONSTANTS FOR A CLASS OF ANALYTIC FUNCTIONS ASSOCIATED WITH A MULTIPLIER LINEAR OPERATOR

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#### Abstract

The purpose of this paper is to find radius constants for a Janowski type

class $H_{k,\mu }^{m}(\lambda ,A,B)$ involving a multiplier linear operator

for functions $f$ satisfying certain conditions on its coefficients. The

sharpness of the results are verified. Some consequent results are also

mentioned.

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Rosihan M. Ali, Nak Eun Cho, Naveen Kumar Jain and V. Ravichandran, Radii of starlikeness and convexity for functions with fixed second coefficient defined by subordination, Filomat, 26(3), (2012), 553-561.

Rosihan M. Ali, S. Nagpal and V. Ravichandran, Second order Differential Subordinations for analytic functions with fixed initial coefficients, Bull. Malays. Math. Sci. Soc., 2(34), (2011), 611-629.

M. K. Aouf and T. M. Seoudy, On differential Sandwich theorems of analytic functions defined by generalized Salagean integral operator, Appl. Math. Lett., (2011), doi:10.1016/j.aml.2011.03.011

L. de Branges, A proof of the Bieberbach conjecture, Acta Mathematica, 154(1-2), (1985), 137-152.

N. E. Cho and T. H. Kim, Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc., 40 (2003), 399-410.

N. E. Cho and H. M. Srivastava, Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling, 37 (2003), 39-49.

P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften 259, Springer, New York, (1983).

T. M. Flett, The The dual of an identity of Hardy and Littlewood and some related inequalities, J. Math. Anal. Appl., 38 (1972), 746-765.

A. Gangadharan and V. Ravichandran, Radii of convexity and strong starlikeness for some classes of analytic functions, Journal of mathematical analysis and applications, 211 (1997), Art. AY975463, 301-313.

V. I. Gavrilov, Remarks on the radius of univalence of holomorphic functions, Akademiya Nauk SSSR: Matematicheskie Zametki, 7 (1970), 295-298.

R. M. Goel, the radius of convexity and starlikeness for certain classes of analytic functions with fixed second coefficients, Ann. Univ. Mariae Curie-Sk lodowska Sect. A, 25 (1971) 33-39.

W. Janowski, Some extremal problems for certain families of analytic functions-I, Annales Polonici Mathematici, 28 (1973), 297-326.

Y. Komatu, On analytical prolongation of a family of operators, Math. (Cluj), 32 (55),

(1990), 141-145.

E. Landau, Der Picard-Schottkysche Satz und die Blochsche Konstante, Sitzungsberichte der Akad. der Wiss. zu Berlin, Phys. Mat. Klass (1925), 467-474.

S. Nagpal and V. Ravichandran, Applications of theory of differential subordination for functions with fixed initial coefficient to univalent functions, Ann. Polon. Math., 105(3), (2012), 225-238.

Mahnaz M. Nargesi, Roshan M. Ali and V. Ravichandran, Radius constants for analytic

functions with fixed second coefficient, The Scientific World J., 2014, Art. ID 898614, 6 pages, (2014).

Z. Nehari, Coformal Mappings, McGraw-Hill, New York, (1952).

F. M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Indian J. Math. Math. Sci., 25-28 (2004), 1429-1436.

M. Obradovic and S. B. Joshi, On certain classes of strongly starlike functions, Taiwanese J. Math., 2(3), (1998), 297-302.

J. Patel, Inclusion relations and convolution properties of certain subclasses of analytic functions defined by a generalized Salagean operator, Bull. Belg. Math. Soc. Simon Stavin, 15 (2008), 33-47.

R. K. Raina and Poonam Sharma, Subordination properties of univalent functions involving a new class of operators, Electr. J. Math. Anal. Appl., 2(1), (2014), 37-52.

R. K. Raina and Poonam Sharma, Subordination preserving properties associated with a class of operators, Le Math. 68(1), (2013), 217-228.

V. Ravichandran, Radii of starlikeness and convexity of analytic functions satisfying certain coefficient inequalities, Math. Slovaca, 64(1), (2014), 27-38.

G. S. Salagean, Subclasses of univalent functions, in Complex Analysis: Fifth Romanian Finnish Seminar, Part I (Bucharest, 1981), Lecture Notes in Mathematics 1013, Springer-

Verlag, Berlin and New York (1983).

Poonam Sharma, Ravinder Krishna Raina and Janusz soko l, Certain subordination results involving a class of operators, Analele Univ. Oradea Fasc. Matematica, 21(2), (2014), 89-99.

D. E. Tepper, On the radius of convexity and boundary distortion of Schlicht functions, Trans. Amer. Math. Soc. 150 (1970), 519-528.

B. A. Uralegaddi and C. Somanatha, Certain classes of univalent functions, in: H.M. Srivastava, S. Owa (Eds.), Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, (1992), 371-374.

S. Yamashita, Radii of univalence, starlikeness, and convexity, Bulletin of the Australian

Mathematical Society, 25(3), (1982), 453-457.

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