Article

# Fixed point theorems for a sum of two mappings in locally convex spaces

International Journal of Mathematics and Mathematical Sciences 01/1994; DOI: 10.1155/S0161171294000967

Source: DOAJ

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**ABSTRACT:**In this article, we establish some fixed point results of Krasnoselskii type for the sum T+S, where S is weakly continuous and T may not be continuous. Some of the main results complement and encompass the previous ones. As an application, we study the existence of solution to one parameter operator equations. Finally, our results are used to prove the existence of solution for integral equations in reflexive Banach spaces.Electronic Journal of Differential Equations. 01/2010; -
##### Article: A topological and geometric approach to fixed points results for sum of operators and applications

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**ABSTRACT:**In this paper, we establish a fixed point result of Krasnoselskii type for the sum A+B, where A and B are continuous maps acting on locally convex spaces. Our results extend previous ones. We apply such results to obtain strong solutions for some quasi-linear elliptic equations with lack of compactness. We also provide an application to the existence and regularity theory of solutions to a nonlinear integral equation modeled in a Banach space. In the last section we develop a sequentially weak continuity result for a class of operators acting on vector-valued Lebesgue spaces. Such a result is used together with a geometric condition as the main tool to provide an existence theory for nonlinear integral equations in Lp(E).Nonlinear Analysis: Theory, Methods & Applications. 01/2005; - [Show abstract] [Hide abstract]

**ABSTRACT:**In this article, we prove some results concerning the Krasnoselskii theorem on fixed points for the sum A + B of a weakly-strongly continuous mapping and an asymptotically nonexpansive mapping in Banach spaces. Our results encompass a number of previously known generalizations of the theorem.Journal of Inequalities and Applications 2011(1). · 0.82 Impact Factor

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