On some subclasses $k$-uniformly Janowski starlike and convex functions associated with $t$-symmetric points

Year 2020, Volume: 49 Issue: 2, 716 - 726, 02.04.2020

Khalida Inayat Noor Nasir Khan Muhammad Arif Janusz Sokol

https://doi.org/10.15672/hujms.588741

Cited By: 2

Abstract

In this paper, we define new subclasses of $k$-uniformly Janowski starlike and $k$-uniformly Janowski convex functions associated with $t$-symmetric points. The integral representations, convolution properties and coefficient bounds for these classes are studied.

Keywords

subordination, convolution, t-symmetric points

References

• [1] M. Arif, K.I. Noor, and R. Khan, On subclasses of analytic functions with respect to symmetrical points, Abst. Appl. Anal. 2012, 790689, 2012.
• [2] R. Chand and P. Singh, On certain schlicht mapping, Indian J. Pure App. Math. 10, 1167–1174, 1979.
• [3] W. Janowski, Some extremal problem for certain families of analytic functions, Ann. Polon. Math. 28 (3), 298–326, 1973.
• [4] S. Kanas and A. Wiśniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105, 327–336, 1999.
• [5] S. Kanas and A. Wiśniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pure. Appl. 45 (4), 647–657, 2000.
• [6] O. Kwon and Y. Sim, A certain subclass of Janowski type functions associated with k-symmetric points, Commun. Korean Math. Soc. 28, 143–154, 2013.
• [7] S.S. Miller and P.T. Mocanu, Differential Subordinations, Theory and Applications, in: Series of Monographs and Textbooks in Pure and Applied Mathematics 225, Marcel Dekker Inc., New York, 2000.
• [8] K.I. Noor and S.N. Malik, On coefficient inequalities of functions associated with conic domains, Comput. Math. Appl. 62, 2209–2217, 2011.
• [9] K.I. Noor and S. Mustafa, Some classes of analytic functions related with functions of bounded radius rotation eith respect to symmetrical points, J. Math. Ineq. 2 (3), 267–276, 2009.
• [10] K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11, 72–75, 1959.
• [11] S. Shams, S.R. Kulkarni, and J.M. Jahangiri, Classes of uniformly starlike and convex functions, Int. J. Math. Math. Sci. 55, 2959–2961, 2004.
• [12] T.N. Shanmugam, C. Ramachandran, and V. Ravichandran, Fekete-Szegö problem for subclass of starlike functions with respect to symmetric points, Bull. Korean Math. Soc. 43 (3), 589–598, 2006.
• [13] H. Silverman, Univalent functions with negative coefficients, Proc. Amr. Math. Soc. 51, 109–116, 1975.
• [14] J. Sokół, Some remarks on the class of functions starlike with respect to symmetric points, Folia Sci. Univ. Tech. Resov. 73, 79–91, 1990.