Coefficient inequalities for Janowski-Sakaguchi type functions associated with conic regions

Year 2018, Volume: 47 Issue: 2, 261 - 271, 01.04.2018

Muhammad Arif Zhi-gang Wang Rafiullah Khan See Keong Lee

https://izlik.org/JA92XS37EY

Abstract

The purpose of the present paper is to introduce and study some new subclasses of Sakaguchi-type functions defined by using the concept of Janowski functions in conic regions. Various interesting properties such as sufficiency criteria, coefficient estimates and distortion result are investigated for these function classes.

Keywords

Sakaguchi-type function , Janowski function , conic domain

References

• M. Arif, S. Mehmood, J. Sokól and J. Dziok, New subclass of analytic functions in conical domain associated with a linear operator, Acta Math. Sci., 36B (2016), 704–7016.
• N. E. Cho, The Noor integral operator and strongly close-to-convex functions, J. Math. Anal. Appl., 283 (2003), 202–212.
• N. E. Cho, O. S. Kwon and H. M. Srivastava, Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl., 292 (2004), 470–480.
• A. W. Goodman, Univalent functions, Vol. I & II, Polygonal Publishing House, Washington, New Jersey, 1983.
• W. Haq and S. Mahmood, Certain properties of a class of close-to-convex functions related to conic domains, Abstr. Appl. Anal., 2013 (2013), 6 pp.
• W. Janowski, Some extremal problems for certain families of analytic functions, Ann. Polon. Math., 28 (1973), 297–326.
• S. Kanas, Techniques of the differential subordination for domains bounded by conic sections, Int. J. Math. Math. Sci., 38 (2003), 2389–2400.
• S. Kanas and A. Wisniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl., 45 (2000), 647–657.
• S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math., 105 (1999), 327–336.
• J.-L. Liu and K. I. Noor, On subordinations for certain analytic functions associated with Noor integral operator, Appl. Math. Comput., 187 (2007), 1453–1460.
• J.-L. Liu and J. Patel, Certain properties of multivalent functions associated with an extended fractional integral operator, Appl. Math. Comput., 203 (2004), 703–713.
• J.-L. Liu and H. M. Srivastava, Certain properties of the Dziok–Srivastava operator, Appl. Math. Comput., 159 (2004), 485–493.
• K. I. Noor and M. Arif, Mapping properties of an integral operator, Appl. Math. Lett., 25 (2012), 1826–1829.
• K. I. Noor, M. Arif and W. Ul-Haq, On k-uniformly close-to-convex functions of complex order, Appl. Math. Comput., 215 (2009), 629–635.
• K. I. Noor and S. N. Malik, On coeffcient inequalities of functions associated with conic domains, Comput. Math. Appl., 62 (2011), 2209–2217.
• S. Owa, T. Sekine and R. Yamakawa, On Sakaguchi type functions, Appl. Math. Comput., 187 (2007), 356–361.
• Y. Polatoglu, Some results of analytic functions in the unit disc, Publ. Inst. Math. (Beograd) (N. S.), 78 (2005), 79–86.
• Y. Polatoglu, S. M. Bolcal and E. Yavuz, A study on the generalization of Janowski functions in the unit disc, Acta Math. Acad. Paedagog. Nyhazi. (N. S.), 22 (2006), 97–105.
• W. Rogosinski, On the coefficients of subordinate functions, Proc. Lodon Math. Soc., 48 (1943), 48–82.
• K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan, 11 (1959), 72–75.
• S. Shams, S. R. Kulkarni and J. M. Jahangiri, Classes of uniformly starlike and convex functions, Int. J. Math. Math. Sci., 55 (2004), 2959–2961.
• H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51 (1975), 109–116.
• H. M. Srivastava, M. R. Khan and M. Arif, Some subclasses of close-to-convex mappings associated with conic regions, Appl. Math. Comput., 285 (2016), 94–102.
• Z.-G. Wang, M. Raza, M. Ayaz and M. Arif, On certain multivalent functions involving the generalized Srivastava-Attiya operator, J. Nonlinear Sci. Appl., 9 (2016), 6067–6076.