Abstract:

The definition of a class of new operators—convex-power 1-set-contraction operators in Banach spaces is given, and the existence of fixed points of this class of operators is studied. By using methods of approximation by operators, the fixed point theorems of Rothe and Altman types convex-power 1-set-contraction operators is obtained, which generalize fixed point theorems of 1-set-contraction operators.

Key words: convex-power 1-set-contraction; fixed point theorem; Banach spaces