Nonexpansive Mappings and Fixed Point Theory in Fuzzy Normed GE-Algebras

In this paper, we investigate the theory of nonexpansive mappings in the framework of fuzzy normed GE-algebras. After recalling the fundamental concepts of GE-algebras and fuzzy GE-norms, we introduce the notion of fuzzy nonexpansive mappings and examine their basic structural properties. We show that the composition of two fuzzy nonexpansive mappings remains fuzzy nonexpansive, and establish that every fuzzy nonexpansive mapping is sequentially continuous with respect to fuzzy convergence. Further, by employing the concept of a fuzzy GE-interpolation family, we define α-averaged mappings in fuzzy normed GE-algebras and prove that such averaged operators preserve nonexpansiveness. We also develop a demiclosedness-type principle and provide fixed point equivalence results between a mapping and its associated averaged mapping under suitable assumptions. Finally, we prove that the fixed point set of a fuzzy nonexpansive mapping is sequentially closed. These results extend classical ideas from metric fixed-point theory and Banach space theory to the algebraic setting of fuzzy normed GE-algebras.