Introduction. Among the most original and far-reaching of the contributions made by Henri Poincaré to mathematics was his introduction of the use of topological or "qualitative" methods in the study of nonlinear problems in analysis. His starting point was the study of the differential equations of celestial mechanics, and in particular of their periodic solutions. His work on this topic began ...

be found in all classical books on the subject (for example in [4, 44]). For every x ∈ X the isotropy subgroup (also termed fixer or stabilizer) of x is Gx = {g ∈ G : gx = x}. If H ⊂ G is a subgroup of G, then the space fixed by H in X is X = {x ∈ X : Hx = x} = {x ∈ X : H ⊂ Gx}. If X and Y are G-spaces, then a G-map (i.e. an equivariant map) f : X → Y is a map which commutes with the G-action: ...

We describe an encoding of major parts of domain theory in the PVS extension of the simply typed calculus these encodings consist of Formalizations of basic structures like partial orders and complete partial orders domains Various domain constructions Notions related to monotonic functions and continuous functions Knaster Tarski xed point theorems for monotonic and continuous functions the pro...

EÎ'(X, A) = Ê\T, H\X, A)) where H denotes the Tate cohomology ofir [l, Chapter 12 ] and H'(X, A) is the jth Cech cohomology group of (X, A) with arbitrary coefficients and with w action induced by that on X. The term Ew is the graded module associated with a certain filtered module J*(XyA). This sequence is natural with respect to ir-equivariant maps of (X, A). If w acts trivially on X, the seq...

We give two examples of the generic approach to fixed point theory. The first example is concerned with the asymptotic behavior of infinite products of nonexpansivemappings in Banach spaces and the second with the existence and stability of fixed points of continuous mappings in finite-dimensional Euclidean spaces.

In this paper some new fixed point theorems of Ky Fan, LeraySchauder and Furi-Pera type are presented for closed multifunctions. AMS Subject Classification. 47H10

The author would like to thank Colegio El Pinar for their hospitality during the preparation of this survey.

This is a brief survey of the use of transfinite induction in metric fixed-point theory. Among the results discussed in some detail is the author’s 1989 result on directionally nonexpansive mappings (which is somewhat sharpened), a result of Kulesza and Lim giving conditions when countable compactness implies compactness, a recent inwardness result for contractions due to Lim, and a recent exte...

in this paper, we prove some approximate fixed point results for proximinal valued $beta$-contractive multifunctions on metric spaces. we show that our results generalize some old fixed point results in the literature.