Fixed Point Theorems for Nonlinear Non-self Mappings in Hilbert Spaces and Applications
نویسندگان
چکیده
Recently, Kawasaki and Takahashi [8] defined a broad class of nonlinear mappings, called widely more generalized hybrid, in a Hilbert space which contains generalized hybrid mappings [9] and strict pseudo-contractive mappings [2]. They proved fixed point theorems for such mappings. In this paper, we prove fixed point theorems for widely more generalized hybrid nonself mappings in a Hilbert space by using an idea of Hojo, Takahashi and Yao [4], and Kawasaki and Takahashi’s fixed point theorems [8]. Using these fixed point theorems for non-self mappings, we proved Browder and Petryshyn’s fixed point theorem [2] for strict pseudo-contractive non-self mappings and Kocourek, Takahashi and Yao’s fixed point theorem [9] for super hybrid nonself mappings. In particular, we solve a fixed point problem.
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