A Fixed Point Theorem for Generalized Lipschitzian Semigroups in Hilbert Spaces

Muhamad Najibufahmi, Atok Zulijanto

Abstract

In this work, we use the concept of a generalized lipschitzian type condition for a semigroup of self mappings as employed in Imdad and Soliman [On uniformly generalized Lipschitzian mappings, Fixed Point Theory Appl. (2002) Article ID 692401] to provide existence theorem of a common fixed point for a left reversible semitopological semigroup of a generalized lipschitzian mappings in a Hilbert space. This result extends and improves a result of Downing and Ray [Uniformly lipschitzian semigroup in Hilbert spaces, Canad. Math. Bull. (1982) 210-214].