In this paper a new class of mappings, known as locally $lambda $-strongly $phi $-accretive mappings, where $lambda $ and $phi $ have special meanings, is introduced. This class of mappings constitutes a generalization of the well-known monotone mappings, accretive mappings and strongly $phi $-accretive mappings. Subsequently, the above notion is used to extend the results of Park and Park, Browder and Ray to locally $lambda $-strongly $phi $-accretive mappings by using Caristi-Kirk fixed point theorem. In the sequel, we introduce the notion of generalized directional contractor and prove a surjectivity theorem which is used to solve certain functional equations in Banach spaces.
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