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Some surjectivity theorems with applications
Archivum mathematicum, Tome 49 (2013) no. 1, pp. 17-27 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2013-1-17
Classification : 47H05, 47H15
Keywords: strongly $\phi $-accretive; locally strongly $\phi $-accretive; locally $\lambda $-strongly $\phi $-accretive; fixed point theorem 
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Pathak, H. K.; Mishra, S. N. Some surjectivity theorems with applications. Archivum mathematicum, Tome 49 (2013) no. 1, pp. 17-27. doi: 10.5817/AM2013-1-17

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