Fixed point theorems for semi-groups of self maps of semi-metric spaces

ABSTRACT. We use selected semi-groups of self maps of a semi-metric space to obtain fixed point theorems for single maps and for families of maps- theorems which generalize results by Browder, Jachymski, Rhoades and Waiters, and others. A basic tool in our approach is the concept of commuting maps. KEY WORDS AND PHRASES: Semi-metric, semi-group, commuting maps, fixed points. 1991 AMS SUBJECT CLASSI]rICATION CODES: Primary 54E25, 54H25. 1. INTRODUCTION. By a semi-group of maps we shall mean a family H of self maps of a set X which is closed with respect to composition of maps. Thus, if f,g E H, then fo g /H. Since composition of maps is associative, H is indeed a semi-group with respect to composition. We shall write fg for f o g and fx for f(x) when convenient and confusion is not likely. We shall utilize the following semi-groups ofmaps in subsequent sections