A new concept of diagonal dominance, which generalizes the strictly diagonally dominance for nonlinear functions, called block diagonal dominance, is introduced. Sufficient conditions for a function to be block strictly diagonally dominant as well as applications to block asynchronous iterative methods for approximating fixed points, are also given.
Generalized diagonally dominant mappings were introduced and studied by A. Frommer [J. Comput. Appl. Math. 38, No. 1-3, 105-124 (1991; Zbl 0746.65046)].