Title: JORDAN *-HOMOMORPHISMS BETWEEN UNITAL C<sup>*</sup>-ALGEBRAS
Abstract:In this paper, we prove the superstability and the generalized Hyers-Ulam stability of Jordan *-homomorphisms between unital <TEX>$C^*$</TEX>-algebras associated with the following functional equation...In this paper, we prove the superstability and the generalized Hyers-Ulam stability of Jordan *-homomorphisms between unital <TEX>$C^*$</TEX>-algebras associated with the following functional equation<TEX>$$f(\frac{-x+y}{3})+f(\frac{x-3z}{c})+f(\frac{3x-y+3z}{3})=f(x)$$</TEX>. Morever, we investigate Jordan *-homomorphisms between unital <TEX>$C^*$</TEX>-algebras associated with the following functional inequality <TEX>$${\parallel}f(\frac{-x+y}{3})+f(\frac{x-3z}{3})+f(\frac{3x-y+3z}{3}){\parallel}\leq{\parallel}f(x)\parallel$$</TEX>.Read More