On Fixed Point Theorems in Banach Spaces Over Topological Semifields

摘要

The notion of topological semifield has been introduced by the mathe- maticians M. Antonovski, V. Boltjanski and T. Sarymsakov in [1]. Let E be a topological semifield and K the set of all its positive elements. Take any two elements x, y in E. If y - x is in K (in K), this is denoted by x y (x < y). As proved in [1], every topological semifield E contains a subsemifield isomorphic to the field R of real numbers.