Sufficient conditions for Janowski starlike functions

Authors

Keywords:

Convex and starlike functions, dfferential subordination, confluent hypergeometric function, Bessel function.

Abstract

Sufficient conditions for confluent (Kummer) hypergeometric function, generalized and normalized Bessel function of the first kind of complex order and integral operator to be subordinate to (1+Az)/(1+Bz) are obtained as applications. Few more applications are discussed.

Mathematics Subject Classification (2010): 30C80, 30C45.

References

Acharya, A.P., Univalence criteria for analytic functions and applications to hypergeometric functions, Ph.D Diss., University of Wurzburg, 1997.

Ali, R.M., Ravichandran, V., Seenivasagan, N., Suffcient conditions for Janowski starlikeness, Int. J. Math. Math. Sci., 2007, Art. ID 62925, 7 pp.

Ali, R.M., Chandrashekar, R., Ravichandran, V., Janowski starlikeness for a class of analytic functions, Appl. Math. Lett., 24(2011), no. 4, 501-505.

Baricz, A., Generalized Bessel Functions of the First Kind, Lecture Notes in Mathematics, 1994, Springer, Berlin, 2010.

Baricz, A., Applications of the admissible functions method for some differential equations, Pure Math. Appl., 13(2002), no. 4, 433-440.

Baricz, A., Geometric properties of generalized Bessel functions, Publ. Math. Debrecen, 73(2008), no. 1-2, 155-178.

Cho, N.E., Kwon, O.S., Ravichandran, V., Coefficient, distortion and growth inequalities for certain close-to-convex functions, J. Inequal. Appl., 2011, 2011:100, 7 pp.

Goodman, A.W., Univalent Functions. Vol. II, Mariner, Tampa, FL, 1983.

Janowski, W., Extremal problems for a family of functions with positive real part and for some related families, Ann. Polon. Math., 23(1970/1971), 159-177.

Lee, S.K., Ravichandran, V., Supramaniam, S., Close-to-convexity and starlikeness of analytic functions, Tamkang J. Math., 46(2015), no. 2, 111-119.

Miller, S.S., Mocanu, P.T., Diffrential subordinations and inequalities in the complex plane, J. Di. Eq., 67(1987), no. 2, 199-211.

Miller, S.S., Mocanu, P.T., The theory and applications of second-order differential subordinations, Studia Univ. Babes-Bolyai Math., 34(1989), no. 4, 3-33.

Miller, S.S., Mocanu, P.T., Dfferential Subordinations, Monographs and Textbooks in Pure and Applied Mathematics, 225, Dekker, New York, 2000.

Polatoglu, Y., Bolcal, M., Some radius problem for certain families of analytic functions, Turkish J. Math., 24(2000), no. 4, 401-412.

Ravichandran, V., Sharma, K., Sufficient conditions for starlikeness, J. Korean Math. Soc., 52(2015), no. 4, 727-749.

Robertson, M.S., Certain classes of starlike functions, Michigan Math. J., 32(1985), no. 2, 135-140.

Ruscheweyh, St., Singh, V., On the order of starlikeness of hypergeometric functions, J. Math. Anal. Appl., 113(1986), no. 1, 1-11.

Ali, R.M., Mondal, S.R., Ravichandran, V., On the Janowski convexity and starlikeness of the confluent hypergeometric function, Bull. Belg. Math. Soc. Simon Stevin, 22(2015),

no. 2, 227-250.

Sharma, K., Ravichandran, V., Applications of subordination theory to starlike functions, Bull. Iranian Math. Soc. (to appear).

Sharma, K., Jain, N.K., Ravichandran, V., Starlike functions associated with a cardioid, Afr. Mat. (2015), available online DOI: 10.1007/s13370-015-0387-7.

Temme, N.M., Special Functions, Wiley, New York, 1996.

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

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Published

2016-03-30

How to Cite

SHARMA, K., & RAVICHANDRAN, V. (2016). Sufficient conditions for Janowski starlike functions. Studia Universitatis Babeș-Bolyai Mathematica, 61(1), 63–76. Retrieved from https://studia.reviste.ubbcluj.ro/index.php/subbmathematica/article/view/5517

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