Common Fixed Points and Invariant Best Approximations in 2-Banach Spaces
DOI:
https://doi.org/10.24237/04.02.732Keywords:
2-Banach Space, Common Fixed Points, 2-f-non-expansive mappingAbstract
In this paper, we introduce and study the concepts of 2-f-contraction and 2-f-nonexpansive mappings in the framework of 2-normed spaces. The main objective is to generalize classical contraction-type mappings and provide an effective approach for analyzing nonlinear problems in such spaces. The methodology is based on extending classical fixed point techniques and employing the properties of 2-normed and 2-Banach spaces under suitable contraction conditions. We establish the existence and uniqueness of a common fixed point for two commuting mappings. In addition, two main results concerning invariant best approximation in 2-Banach spaces are obtained. The results extend and improve several known theorems and demonstrate the applicability of the proposed approach in fixed point theory and approximation problems in 2-normed and 2-Banach spaces.
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