In this paper a new class of mappings, known as locally λ-strongly φ-accretive mappings, where λ and φ have special meanings, is introduced. This class of mappings constitutes a generalization of the well-known monotone mappings, accretive mappings and strongly φ-accretive mappings. Subsequently, the above notion is used to extend the results of Park and Park, Browder and Ray to locally λ-stron...