# Article

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Keywords:
strongly $\phi$-accretive; locally strongly $\phi$-accretive; locally $\lambda$-strongly $\phi$-accretive; fixed point theorem
Summary:
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.
References:
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