A New Extension Theorem for Concave Operators

作者：Peng Jian wen^*; Rong Wei dong; Yao Jen Chih

来源：Fixed Point Theory and Applications, 2009, 2009(1): 571546.

DOI：10.1155/2009/571546

We present a new and interesting extension theorem for concave operators as follows. Let X be a real linear space, and let (Y, K) be a real order complete PL space. Let the set A subset of X x Y be convex. Let X(0) be a real linear proper subspace of X, with. theta is an element of (A(X) - X(0))(ri), where A(X) = {x vertical bar (x, y) is an element of A for some y is an element of Y}. Let g(0) : X(0) -> Y be a concave operator such that g(0)(x) <= z whenever (x, z) is an element of A and x is an element of X(0). Then there exists a concave operator g : X -> Y such that (i) g is an extension of g(0), that is, g(x) = g(0)(x) for all x is an element of X(0), and (ii) g(x) <= z whenever (x, z) is an element of A.

• 出版日期2009
• 单位重庆师范大学; 内蒙古大学; 中山大学