A Fixed Point Theorem for Sum of Operators and Applications
نویسندگان
چکیده
In the present paper we establish a fixed point result of Krasnoselskii type for the sum A+B, where A and B are sequentially weakly continuous, and B is a nonexpansive mapping. As an application, we study the existence of solutions for an nonlinear integral equation in Banach spaces. 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 as the main tool to provide an existence theory for integral equations in L(E).
منابع مشابه
A new characterization for Meir-Keeler condensing operators and its applications
Darbo's fixed point theorem and its generalizations play a crucial role in the existence of solutions in integral equations. Meir-Keeler condensing operators is a generalization of Darbo's fixed point theorem and most of other generalizations are a special case of this result. In recent years, some authors applied these generalizations to solve several special integral equations and some of the...
متن کاملOn intermediate value theorem in ordered Banach spaces for noncompact and discontinuous mappings
In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...
متن کاملApplication of measures of noncompactness to infinite system of linear equations in sequence spaces
G. Darbo [Rend. Sem. Math. Univ. Padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. In this paper, we apply the Darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.
متن کاملA strong convergence theorem for solutions of zero point problems and fixed point problems
Zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated. A strong convergence theorem for the common solutions of the problems is established in the framework of Hilbert spaces.
متن کاملRemarks on the Paper ``Coupled Fixed Point Theorems for Single-Valued Operators in b-Metric Spaces''
In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by Bota et al. [M-F. Bota, A. Petrusel, G.Petrusel and B. Samet, Coupled fixed point theorems forsingle-valued operators in b-metric spaces, Fixed Point TheoryAppl. (2015) 2015:231]. Also, we prove that Perov-type fix...
متن کاملSimultaneous generalizations of known fixed point theorems for a Meir-Keeler type condition with applications
In this paper, we first establish a new fixed point theorem for a Meir-Keeler type condition. As an application, we derive a simultaneous generalization of Banach contraction principle, Kannan's fixed point theorem, Chatterjea's fixed point theorem and other fixed point theorems. Some new fixed point theorems are also obtained.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004