Convergence theorem for finite family of lipschitzian demi-contractive semigroups

Abstract

Abstract Let E be a real Banach space and K be a nonempty, closed, and convex subset of E. Let be a finite family of Lipschitzian demi-contractive semigroups of K, with sequences of bounded measurable functions Li : [0, ∞) → (0, ∞) and bounded functions λi : [0, ∞) → (0, ∞), respectively, where , i = 1,2, ..., N. Strong convergence theorem for common fixed point for finite family is proved in a real Banch space. As an application, a new convergence theorem for finite family of Lipschitzian demi-contractive maps is also proved. Mathematics subject classification (2000) 47H09, 47J25

Keywords

• Demi-contractive maps
• Demi-contractive semigroup
• Demicompact maps
• Fixed point