International Electronic Journal of Pure and Applied Mathematics —————————————————————————————— Volume 7 No. 3 2014, 99-107 ISSN: 1314-0744 url: http://www.e.ijpam.eu doi: http://dx.doi.org/10.12732/iejpam.v7i3.1 FIXED-POINTS AND UNIQUENESS OF ENTIRE AND MEROMORPHIC FUNCTIONS Harina P. Waghamore 1 , A. Tanuja 2 § , N. Shilpa 3 1,2 Department of Mathematics Central College Campus Bangalore University Bangalore, 560 001, INDIA 3 Department of Mathematics M.E.S. Degree College Malleswaram, Bangalore, 560 003, INDIA Abstract: In this paper, we deal with the uniqueness problems on entire and meromorphic functions concerning differential polynomials that share fixed-points. These results improve and extend those given by Xiaojuan Li and C. Meng, see [2]. AMS Subject Classification: 30D35 Key Words: entire functions, meromorphic functions, fixed-points, uniqueness 1. Introduction In this paper, we use the standard notations and terms in the value distribution theory [4]. For any nonconstant meromorphic function f (z) on the complex plane C , we denote by S (r, f ) any quantity satisfying S (r, f )= o{T (r, f )}, as r → +∞, except possibly for a set of r of finite linear measures. A meromorphic function a(z) is called a small function with respect to f (z) if T (r, a)= S (r, f ). Let S (f ) be the set of meromorphic function in the complex plane C which are small functions with respect to f . Set E(a(z),f )= {z : f (z) − a(z)=0}, a(z) ∈ S (f ), where a zero Received: July 11, 2013 c  2014 Academic Publications, Ltd. § Correspondence author International Electronic Journal of Pure and Applied Mathematics – IEJPAM, Volume 7, No. 3 (2014)