We show that every rotation of an even-dimensional sphere must have a fixed point.

Using Poincaré duality in K-theory, we state and prove a Lefschetz fixed point formula for endomorphisms of cross product C-algebras C0(X)⋊G coming from covariant pairs. Here G is assumed countable, X a manifold, and X ⋊ G cocompact and proper. The formula in question expresses the graded trace of the map on rationalized K-theory of C0(X) ⋊G induced by the endomorphism, i.e. the Lefschetz numbe...

In this paper, the existence of the fixed point of fuzzy sequence of successive approximations is proved. For this idea, the   distance is defined and some theorems are proved in detail.

In this note, we prove common fixed point for a Banach pair of mappings on D∗-Generalized Cone Metric Space.

We prove existence results for discontinuous functional equations in general L-spaces and apply these results to the solvability of implicit and explicit elliptic boundary-value problems involving discontinuous nonlinearities. The main tool in the proof is a fixed point result in lattice-ordered Banach spaces proved by the second author.

The purpose of this paper is to introduce the concept of the homeomorphism metric space and to prove the fixed point theorems and the best proximity point theorems for generalized contractions in such spaces. The multiplicative metric space is a special form of the homeomorphism metric space. The results of this paper improve and extend the previously known ones in the literature. c ©2017 All r...

We present a positive solution to McColm’s conjecture for the special case of decidable theories. This gives a uniform explanation of the separation of fixed-point from first-order definability over a wide range of commonly studied classes of finite structures (including ordered ones). We demonstrate why this result generalizes the standard constructive proofs, and show why it is unlikely that ...

The purpose of this paper is to study common fixed points in complex valued metric spaces and obtain sufficient conditions for the existence of common fixed points of a pair of mappings satisfying generalized contraction involving rational expressions.

We define the category of manifolds with extended tangent bundles, we study their symmetries and we consider the analogue of equivariant cohomology for actions of Lie groups in this category. We show that when the action preserves the splitting of the extended tangent bundle, our definition of extended equivariant cohomology agrees with the twisted equivariant de Rham model of Cartan, and for t...

*Correspondence: [email protected] 3Department of Mathematics, Jiangxi University of Finance and Economics, Nanchang, 330013, China Full list of author information is available at the end of the article Abstract In this paper, we introduce the concept of JS-quasi-contraction and prove some fixed point results for JS-quasi-contractions in complete metric spaces under the assumption that the ...