Approximate Endpoints for Set-Valued Contractions in Metric Spaces

Abstract

The existence of approximate fixed points and approximate endpoints of the multivalued almost -contractions is established. We also develop quantitative estimates of the sets of approximate fixed points and approximate endpoints for multivalued almost -contractions. The proved results unify and improve recent results of Amini-Harandi (2010), M. Berinde and V. Berinde (2007), Ćirić (2009), M. Păcurar and R. V. Păcurar (2007) and many others.