We prove that a convex subcomplex of a spherical building of type E7 or E8 is a subbuilding or the group of building automorphisms preserving the subcomplex has a fixed point in it. Together with previous results of Mühlherr-Tits, and Leeb and the author, this completes the proof of Tits’ Center Conjecture for thick spherical buildings.

When G is a profinite group and H and K are closed subgroups, with H normal in K, it is not always possible to form the iterated homotopy fixed point spectrum (ZhH)hK/H , where Z is a continuous G-spectrum. However, we show that, if G = Gn, the extended Morava stabilizer group, and Z = L̂(En ∧ X), where L̂ is Bousfield localization with respect to Morava K-theory, En is the Lubin-Tate spectrum, a...

In this investigation, we have established the existence and uniqueness results of solutions for class of an abstract fractional functional integro-differential equations with state dependent delay subject to not instantaneous impulse by using fixed point theorems. One example is presented to illustrate the main results of the paper. MSC: 26A33 • 34K05 • 34A12 • 26A33

We show that the fixed point set of a proper action of a Lie group G on a Poisson manifold M by Poisson automorphisms has a natural induced Poisson structure and we give several applications.

Let x = x0x1 ... be a fixed point of a substitution on the alphabet {a,b}, and let Ua = (-10 -11) and Ub = (10 11) We give a complete classification of the substitutions 03C3 : {a, b}* ~ {a, b}* according to whether the sequence of matrices (Ux0 Ux1... Uxn)~n=0 is bounded or unbounded. This corresponds to the boundedness or unboundedness of the oriented walks generated by the substitutions.

In this paper, we prove some common fixed point theorems for co-cyclic weak contractions in compact metric spaces. Keywords—Cyclic weak contraction, Co-cyclic weak contraction, Co-cyclic representation, Common fixed point.

Recently, Bucur, Guran and Petruşel presented some results on fixed point of multivalued operators on generalized metric spaces which extended some old fixed point theorems to the multivalued case ([1]). In this paper, we shall give some results on fixed points of multivalued operators on ordered generalized metric spaces by providing different conditions in respect to [1].

Let (X,1) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Let F : X ×X Ã X be a mixed monotone set valued mapping. We obtain sufficient conditions for the existence of a coupled fixed point of F.

This paper concerns an inverse problem for an integro-differential equation related to the Basset problem. The inverse problem aims to determine a weakly singular term from the time trace at a fixed point x0 ∈ . We use the maximum principle for an integro-differential operator to derive the uniqueness of the inverse problem. Additionally, we prove the existence and uniqueness of the direct Bass...

We study the action of pseudo-Anosov homeomorphisms f : R → R on the character varieties of SL(2,C) -representations of the fundamental groups π1(R) of closed orientable hyperbolic surfaces R . We prove that the representation π1(R) →֒ SL(2,C) corresponding to the holonomy representation of the hyperbolic structure on the mapping torus of f is a hyperbolic fixed point for the action of f on the ...