Journal of Quality Measurement and Analysis Jurnal Pengukuran Kualiti dan Analisis ON FEKETE-SZEGÖ PROBLEMS FOR A SUBCLASS OF ANALYTIC FUNCTIONS (Berkenaan Permasalahan Fekete-Szegö bagi Subkelas Fungsi Analisis) ENTISAR EL-YAGUBI & MASLINA DARUS ABSTRACT The aim of this paper is to determine the Fekete-Szegö inequalities for a normalised analytic function f ( z ) defined on the open unit disc for which z ( D λ 1 ,λ 2 ,δ m,b f ( z ) ′ ) /( D λ 1 ,λ 2 ,δ m,b f ( z )), δ , m, b ∈N 0 , λ 2 ≥ λ 1 ≥ 0 lies in a region starlike with respect to 1 and it is symmetric with respect to the real axis by using the operator D λ 1 ,λ 2 ,δ m,b f ( z ) given recently by the authors. As a special case of this result, Fekete-Szegö inequality for a class of functions defined by fractional derivatives is also obtained. Keywords: analytic function; starlike function; subordination; Fekete-Szegö inequality; derivative operator ABSTRAK Matlamat makalah ini adalah untuk menentukan ketaksamaan Fekete-Szegö bagi fungsi analisis ternormal yang ditakrif pada cakera unit terbuka dengan z ( D λ 1 ,λ 2 ,δ m,b f ( z ) ′ ) /( D λ 1 ,λ 2 ,δ m,b f ( z )), λ 2 ≥ λ 1 ≥ 0, δ , m, b ∈N 0 terletak pada rantau bak bintang terhadap 1 dan simetri terhadap paksi nyata dengan menggunakan pengoperasi D λ 1 ,λ 2 ,δ m,b f ( z ) yang diberi penulis baru-baru ini. Sebagai kes khas bagi hasil ini, ketaksamaan Fekete-Szegö bagi kelas fungsi yang ditakrif oleh terbitan pecahan juga diperoleh. Kata kunci: fungsi analisis; fungsi bak bintang; subordinasi; ketaksamaan Fekete-Szegö; pengoperasi terbitan 1. Introduction Let A denote the class of functions of the form f ( z ) = z + n=2 ∞ ∑ a n z n ,( z ∈U ), (1) which are analytic in the open unit disc U = {z : z ∈C,| z |< 1}. Also, let S be the subclass of A consisting of all functions, which are univalent in U . Let φ ∈ P, where φ ( z ) is an analytic function with positive real part on A with φ (0) = 1, ′ φ (0) > 0, and let S * (φ ) be the class of functions in f ∈A such that z ′ f ( z ) f ( z ) ≺ φ ( z ), ( z ∈U ), (2) and C (φ ) be the class of functions in f ∈A for which JQMA 10(1) 2014, 17-26