เอกสารประชุมวิชาการระดับขาติมหาวิทยาลัยทักษิณ ครั้งที่ 28 2561

1094 การประชุมวิชาการระดับชาติมหาวิทยาลัยทักษิณ ครั้งที่ 28 ประจ�าปี 2561 Result Theorem. Let C be a nonempty closed and convex subset of a uniformly convex Banach space 9 endowed with a directed graph ( such that 7 ( C and E ( is convex. The mappings 1 2 3 J T J are G-nonexpansive from C into itself. Assume that 3 1 J J F : F T ˆ is nonempty and closed subset of C . For an initial point  0 x C , define the sequence ^ ` O x in C as follows: D D D D D D 1 1 1 1 2 2 2 3 3 3 1 1 1 O O O O O O O O O O O O O O O x x T Z Z x T [ [ x T x (3) Where ^ ` 3 1 O J J D are real sequences in ª º ¬ ¼ 1 D D for some D  10 2 . If the graph ( is transitive and 1 2 3 J T J satisfy condition (II). Then the sequence ^ ` O x converges strongly to a common fixed point of F . Proof. We first show that O O O O O O O O O O x V Z V [ V V x V Z V [ x Z Z [ and O O x [ are in E ( . For  V F and  0 0 0 x V Z V [ V E ( and 1 2 3 J T J are edge-preserving. Then we have  1 0 2 0 3 0 T Z V T [ V T x V E ( . By the convexity of E ( and 1 0 0 T Z V x V  E ( , we have  1 x V E ( . By edge-preserving of 3 T , then  3 1 T x V E ( . By the convexity of E ( and 3 1 1 T x V x V  E ( , we have  1 [ V E ( . By edge-preserving of 2 T , then  2 1 T x V E ( . By the convexity of E ( and 2 1 1 T x V [ V  E ( , we have  1 Z V E ( . For  L L L x V Z V [ V E ( . Since E ( is convex and 1 2 3 J T J are edge-preserving. Then  1 2 3 L L L T Z V T [ V T x V E ( . Since L x V and  1 L T Z V E ( and E ( is convex, then we get 1 1 1 1 1 1 1 1 1 L L L L L L L L L x V T Z V x T Z V x V E ( D D D D  (4) By edge-preserving of 3 T , then 3 1 L T x V E (  . Since 3 1 1 L L T x V x V E (  and E ( is convex, we get 3 1 3 3 1 3 1 3 3 1 1 1 1 L L L L L L L L L x V T x V x T x V [ V E ( D D D D  . (5)