Fixed Point Theory and Generalized Leray–schauder Alternatives for Approximable Maps in Topological Vector Spaces
نویسندگان
چکیده
Some new fixed point theorems for approximable maps are obtained in this paper. Homotopy results, via essential maps, are also presented for approximable maps.
منابع مشابه
Generalized Leray–schauder Principles for Compact Admissible Multifunctions
We establish the Leray–Schauder type theorems for very general classes of multifunctions, which are called admissible. Our admissible classes contain compositions of important multifunctions in nonlinear analysis and algebraic topology. Moreover, our arguments are elementary, without using the concept of degree of maps or theory of homotopy extensions. The Leray–Schauder principle [LS], one of ...
متن کاملFixed Point Theory for Admissible Type Maps with Applications
In this paper, assuming a natural sequentially compact conditionwe establish new fixed point theorems for Urysohn type maps between Fréchet spaces. In Section 2 we present new LeraySchauder alternatives, Krasnoselskii and Lefschetz fixed point theory for admissible type maps. The proofs rely on fixed point theory in Banach spaces and viewing a Fréchet space as the projective limit of a sequence...
متن کاملA Leray-schauder Alternative for Weakly-strongly Sequentially Continuous Weakly Compact Maps
This paper presents new fixed point results for weakly sequentially upper semicontinuous maps defined on locally convex Hausdorff topological spaces which are angelic when furnished with the weak topology. Moreover, we establish an applicable Leray-Schauder alternative (Theorem 2.12) for a certain subclass of these maps. Our alternative combines the advantages of the strong topology (i.e., the ...
متن کاملThe Topological Degree for Noncompact Nonlinear Mappings in Banach Spaces
Let X and Y be Banach spaces, G an open subset of X. If we denote the closure of G by cl(G), let ƒ be a mapping of cl(G) into Y. For X~ Y and ƒ a compact mapping, Leray and Schauder [9] gave a definition of topological degree for mappings of the form ƒ —ƒ on the open set G over a point a of X whenever (I—f)"^) is a compact subset of G. The Leray-Schauder degree for compact displacements is the ...
متن کاملRandom Approximation and Random Fixed Point Theory for Random Non–self Multimaps
This paper presents new random fixed point theorems and random Leray–Schauder alternatives for a variety of maps (e.g., Bκ, Uκ c , KKM and PK maps). A random Kransnoselskii cone compression theorem for Uκ c maps is also given. Various random approximation theorems for the above classes are proved and as applications several random fixed point theorems are also derived.
متن کامل