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In this paper, we prove the following generalization of the classical Darbo fixed point principle : Let X be a Banach space and µ be a montone measure of noncompactness on X which satisfies the generalized Cantor intersection property. Let C be a nonempty bounded closed convex subset of X and T : C → C be a continuous mapping such that for any countable set Ω ⊂ C, we have µ(T(Ω)) ≤ kµ(Ω), where k is a constant, 0 ≤ k < 1. Then T has at least one fixed point in C. The proof is based on a combined use of topological methods and partial ordering techniques and relies on the Schauder and the Knaster-Tarski fixed point principles.

In this paper we prove some new fixed point theorems in r-normed and locally r-convex spaces. Our conclusions generalize many well-known results and provide a partial affirmative answer to Schauder's conjecture. Based on the obtained results, we prove the analogue of a Von Neumann's theorem in locally r-convex spaces. In addition, an application to game theory is presented. [ABSTRACT FROM AUTHOR]

Abstract We present some fixed point theorems for the sum of a weakly-strongly continuous map and a nonexpansive map on a Banach space . Our results cover several earlier works by Edmunds, Reinermann, Singh, and others.

Abstract We present new fixed point theorems for ws-compact operators. Our fixed point results are obtained under Sadovskii, Leray-Schauder, Rothe, Altman, Petryshyn, and Furi-Pera type conditions. An example is given to show the usefulness and the applicability of our results.

This paper deals with a new existence theory for periodic solutions to a broad class of evolution equations. We first establish new fixed point theorems for affine maps in locally convex spaces and ordered Banach spaces. Our new fixed point results extend, encompass and complement a number of well-known theorems in the literature, including the famous Chow and Hale fixed point theorem. With these obtained fixed point results, we investigate the existence of periodic solutions for some class of nonhomogeneous linear systems in Banach spaces with lack of compactness. Some illustrative examples are also given. [ABSTRACT FROM AUTHOR]