เอกสารประชุมวิชาการระดับขาติมหาวิทยาลัยทักษิณ ครั้งที่ 28 2561

1092 การประชุมวิชาการระดับชาติมหาวิทยาลัยทักษิณ ครั้งที่ 28 ประจ�าปี 2561 Definition 3. [5] Let C be a nonempty closed bounbed subset of a uniformly convex Banach space 9 . The mappings  1 2 3 T T T : C C with ˆ z‡ 3 1 J J F : F T are said to satisfy Condition (II) if there is a non-decreasing function > > f  f 0 0 G : with ! 0 0 0 G G S for  f 0 S such that ^ ` t 1 2 3 NBx E x T x E x T x E x T x G E x F T for all  x C . Let C be a nonempty subset of a real Banach space 9 and ' denote diagonal of the cartesian product u C C . Consider a directed graph ( 7 ( E ( such that the set 7 ( of its vertices coincides with C and the set E ( of its edges with ' E ( . We assume ( has no parallel edges. A weighted graph is a graph in which a number (the weight) is assigned to each edge. The conversion of a graph ( in the graph obtained from ( by reversing the direction of edges denoted by 1 ( , and ^ `  1 E ( x Z : Z x E ( . Let x and Z be vertices of a graph ( . A path in ( from x to Z of length ^ `  ‰ 0 / is a sequence ^ ` 0 / J J x of 1 / vertices for which 0 / x x x Z and  1 J J x x E ( for 1 2 1 J / . A graph ( is said to be connected if there is a path between any two vertices of the graph ( , In a directed graph, an ordered pair of vertices x Z is call strongly connected if a directed path leads from x to Z Otherwise, the ordered pair is called weakly connected if an undirected path leads from x to Z after replacing all of its directed edges with undirected edges. A directed graph ( 7 ( E ( is said to be transitive if, for any  x Z [ 7 ( such that x Z and Z [ are in E ( , we have  x [ E ( . Let C be a nonempty convex subset of a real Banach space, ( 7 ( E ( be a directed graph such that 7 ( C and  T : C C . Then T is said to be G-nonexpansive (see [6]) if the following conditions hold: (i) T preserves edges of ( , i.e.,     x Z E ( Tx TZ E ( x Z C ; (ii) T non-increases weights of edges of ( in the following way: d   Tx TZ x Z XIFOFWFS x Z E ( GPS BOZ x Z C . Example 4. [7] Let D be the Banach space of convergent sequences and ! 1 L . Let ( E E ( , where 9 D and ^ O O E ( x Z for all   O O O x Z and ` t 1 2 O O Z x O .