Abstract:The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear operator equation F(x) = αx (α ≥ 1) for so-called 1-set weakly contractive operators on unbounded domains in Banach spaces. We also introduce the concept of weakly semi-closed operator at the origin and obtain a series of new fixed point theorems and the existence theorems for the nonlinear operator equation F(x) = αx (α ≥ 1) for such class of operators. As consequences, the main results… Show more
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