เอกสารประชุมวิชาการระดับขาติมหาวิทยาลัยทักษิณ ครั้งที่ 28 2561

1093 งานวิจัยและนวัตกรรมเพื่อสังคมที่มั่นคง มั่งคั่ง และยั่งยืน (Research and Innovation for Social Stability, Prosperity and Sustainability) Define a mapping  T : 9 9 by   ®   ¯ 2 3 4 1 2 3 1 2 3 0 O J O x x x JG x GPS BMM O T x x x x Lx Lx Lx JG x GPS TPNF O Note that T is G-nonexpansive. Xu and Noor [8] introduced and studied a three-step scheme to approximate fixed point of in Banach space. The study of fixed point theorem in Banach spaces were investigated by many authors (see [5] [9] [10] [12] [13]). In 2008, Jachymski [14] proved generalizations of the Banach’s contraction principle in complete metric spaces endowed with a graph. In 2015, Tiammee et al. [7] proved Browder’s convergence theorem for G-nonexpansive mappings in Hilbert spaces with a directed graph. The study of fixed point theorem for G-nonexpansive mappings in Hilbert spaces and Banach spaces were investigated by many authors (see [7] [15] [16]). Recently, Suparatulatorn et al. [17] proved a strong convergence theorem for two different hybrid methods by using CQ method for a finite family of G-nonexpansive mappings in a Hilbert space. Motivated by [8] and [17], we construct a new three-step scheme for G-nonexpansive mappings in uniformly convex Banach space 9 endowed with a graph and we prove the strong convergence theorem under the appropriate condition. Materials and Methodology 1. Studying and investigating on the fixed point problem. 2. Studying and investigating on graph theory. 3. Studying and investigating on the G-nonexpansive mapping. 4. Establishing a new theorem of the fixed point problem for G-nonexpansive mappings in Banach spaces.