Certain classes of $k$-uniformly functions with bounded radius rotation associated with linear operator

Year 2020, Volume: 49 Issue: 1, 56 - 67, 06.02.2020

Shahid Mehmood Saima Mustafa

https://doi.org/10.15672/HJMS.2018.651

Abstract

In this paper we use linear operator to define certain classes of analytic functions related to conic domains. Inclusion results, radius problems, rate of growth and other interesting properties are investigated.

Keywords

subordination, functions with positive real part, linear operator, conic domain, starlike and convex functions

References

• [1] M. Arif, S. Mahmood, J. Sokołand J. Dziok, New subclass of analytic functions in conical domain associated with a linear operator, Acta Math Sci, 36B(3), 1–13, 2016.
• [2] M. Arif, S. Umar, S. Mahmood and J. Sokoł, New reciprocal class of analytic functions associated with linear operator, Iran. J. Sci. Technol. Trans. Sci., 42, 881–886, 2018.
• [3] D.A. Brannan, On functions of bounded boundary rotations, Proc. Edinb. Math. Soc. 2, 339–347, 1968–1969.
• [4] G. Golusin, On distortion theorems and coefficients of univalent functions, Rec. Math. [Mat. Sbornik] N.S., 19 (61), 183–202, 1946.
• [5] A.W. Goodman, Univalent functions, Vol. I, II, Polygonal Publishing House, Wash- ington, New Jersey, 1983.
• [6] A.W. Goodman, On uniformly convex functions, Ann. Polon. Math. 56, 87–92, 1991.
• [7] S. Kanas, Techniques of the differential subordination for domains bounded by conic sections, Int. J. Math. Math. Sci. 38, 2389–2400, 2003.
• [8] S. Kanas and A. Lecko, Differential subordination for domains bounded by hyperbolas, Zeszyty Nauk. Politech. Rzeszowskiej Mat. 175 (23), 61–70, 1999.
• [9] S. Kanas and A. Wisniowska Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105, 327–336, 1999.
• [10] S. Kanas and A. Wiśniowska, Conic regions and k-starlike functions, Rev. Roumaine, Math. Pures Appl. 45, 647–657, 2000.
• [11] S. Mahmood and J. Sokoł, New subclass of analytic functions in conical domain as- sociated with ruscheweyh Q-differential operator, Results Math. 71, 1345–1357, 2017.
• [12] S. Mahmood, S.N. Malik, S. Mustafa and S.M.J. Riaz, A new subclass of k-Janowski type functions associated with Ruscheweyh derivative, J. Func. Spaces, 2017, Article ID 6095293, 7 pages, 2017.
• [13] S.S. Miller and P.T. Mocanu, Differential subordinations theory and applications, Marcel Dekker, Inc. New York Basel, 2000.
• [14] K.I. Noor, Higher order close-to-convex functions, Math. Japon. 37, 1–8, 1992.
• [15] K.I. Noor, On a generalization of uniformly convex and related functions, Comp. Math. Appl. 61, 117–125, 2011.
• [16] K.I. Noor and S.N. Malik, On a new class of analytic functions associated with conic domain, Comput. Math. Appl. 62, 367–375, 2011.
• [17] K.I. Noor and S.N. Malik, On coefficient inequalities of functions associated with conic domains, Comput. Math. Appl. 62, 2209–2217, 2011.
• [18] B. Pinchuk, Functions with bounded boundary rotation, Isr. J. Math. 10, 7–16, 1971.
• [19] R.K. Raina and P. Sharma, Subordination properties of univalent functions involving a new class of operators, Electron. J. Math. Anal. Appl. 2 (1), 37–52, 2014.
• [20] F. Rønning, Uniformly convex functions and a corresponding class of starlike func- tions, Proc. Amer. Math. Soc. 118, 189–196, 1993.
• [21] P. Sharma, R.K. Raina and J. Sokoł, Certain subordination results involving a class of operators, Analele Univ. Oradea Fasc. Matematica, 21 (2), 89–99, 2014.