Some aspects of the n-ary orthogonal and b(αn,βn)-best approximations of b(αn,βn)-hypermetric spaces over Banach algebras

In this article, a definition of a b(αn,βn){b}_{\left({\alpha }_{n},{\beta }_{n})}-best approximations of b(αn,βn){b}_{\left({\alpha }_{n},{\beta }_{n})}-hypermetric spaces over Banach algebras is given. Our objective is to prove the concept of extension of fixed point theorems in nn-ary orthogonal b(αn,βn){b}_{\left({\alpha }_{n},{\beta }_{n})}-hypermetric spaces over Banach algebras.