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The purpose of this paper is to introduce a concept of Tf-orbitally lower semi-continuous mappings which is more general than the concept of T-orbitally lower semi-continuous mappings and continuous mappings and also prove Mizoguchi-Takahashi’s type coincidence point theorems by using this concept. Moreover, we show that the existence of common fixed points for Mizoguchi-Takahashi’s type multi-valued mappings do not require the condition of T-weakly commuting mappings. Finally, some invariant approximation results are obtained as applications. Our results unify, extend, and complement several well-known results.

Mizoguchi-Takahashi’s type common fixed point theorems without T-weakly commuting condition and invariant approximations