Approximation of set valued functions and fixed point theorems

Sommario Il risultato fondamentale della Nota è il seguente: siaΓ una multiapplicazione semicontinua superiormente da uno spazio metrico compatto S ad uno spazio normato Y, tale cheΓ(x) è convesso. Allora per ogniɛ>0 esiste una applicazione continua f: :S → Y tale che d*(F, G)<ɛ, ove F e G sono i grafici di f eΓ e d*(F, G)=sup {d(y, G), y ∈ F}. Come corollari di questo teorema vengono dimostrati il teorema di punto fisso di Kakutani in uno spazio di Banach ed una sua generalizzazione, che non richiede la compattezza diΓ(x). Viene poi presentato un teorema di punto fisso con condizioni di convessità più deboli di quello di Kakutani.

---

---

Entrata in Redazione il 14 gennaio 1969.

---

This work was performed while the author held the position of Faculty Research Assistant at the University of Maryland and was partially supported by the National Science Foundation under Grant GP-7846.     

Some generalizations of fixed point theorems and common fixed point theorems

We present some fixed point theorems and common fixed point theorems which generalize and unify previous known results.     

Fixed point theorems for discontinuous mapping

We prove a generalization of Brouwer's famous fixed point theorem to discontinuous maps. The main result shows that for discontinuous functions on a compact convex domainX one can always find a pointx X such that x–f(x) is less than a certain measure of discontinuity. Applications to artificial neural nets, economic equilibria and analysis are given.     

Chebysev-中心和不动点定理

本文利用Chebysev—中心讨论了Banach空间Z中广义非扩张映象的不动点定理以及广义压缩映象不动点的迭代逼近。     

Minimax and fixed point theorems

Mathematische Annalen -     

一类单调算子的不动点定理

研究了范围广泛的半闭1-集压缩算子及凝聚算子,获得了一些新的不动点定理,所获结果推广了已知的结论.     

Generalized KKM theorems and common fixed point theorems

In this paper, we first prove a generalized KKM theorem, and then use this generalized KKM theorem to establish the generalized equi-KKM theorem, common fixed point theorems for a family of multivalued maps, and the Kakutani-Fan-Glicksberg fixed point theorem. We also show that an existence theorem of the common fixed point theorem is equivalent to the Kakutani-Fan-Glicksberg fixed point theorem.     

Acceleration method for convex optimization over the fixed point set of a nonexpansive mapping

Mathematical Programming - The existing algorithms for solving the convex minimization problem over the fixed point set of a nonexpansive mapping on a Hilbert space are based on algorithmic...     

On fixed point theorems and nonsensitivity

Sensitivity is a prominent aspect of chaotic behavior of a dynamical system. We study the relevance of nonsensitivity to fixed point theory in affine dynamical systems. We prove a fixed point theorem which extends Ryll-Nardzewski??s theorem and some of its generalizations. Using the theory of hereditarily nonsensitive dynamical systems we establish left amenability of Asp(G), the algebra of Asplund functions on a topological group G (which contains the algebra WAP(G) of weakly almost periodic functions). We note that, in contrast to WAP(G) where the invariant mean is unique, for some groups (including the integers) there are uncountably many invariant means on Asp(G). Finally, we observe that dynamical systems in the larger class of tame G-systems need not admit an invariant probability measure, and the algebra Tame(G) is not left amenable.     

Fuzzy mappings and fixed point theorems

We extend Heilpern's fixed point theorem for fuzzy contraction mappings to a pair of generalized fuzzy contraction mappings. Also we prove a fixed point theorem for nonexpansive fuzzy mappings on a compact star-shaped subset of a Banach space.