The Lefschetz Fixed Point Theorem generalizes a collection of fixed point theorems for different topological spaces, including maps on the n-sphere and the n-disk. Although the theorem is easily written in terms of compact manifolds, in this paper we will work entirely with topological spaces that are simplicial complexes or retracts of simplicial complexes. After developing the fundamentals of...

In this paper we extend some existing results and prove fixed point theorem on partially ordered cone metric spaces which satisfy certain weak contractive inequalities. In this consequence we have also given some illustrative examples.

In this paper, we prove some common fixed point theorems for two pair of compatible and subsequentially continuous mappings satisfying an implicit relation in Modified Intuitionistic fuzzy metric spaces. Consequently, our results improve and sharpen many known common fixed point theorems available in the existing literature of metric fixed point theory.

In 1994, S.G. Matthews introduced the notion of a partial metric space and obtained, among other results, a Banach contraction mapping for these spaces. Later on, S.J. O’Neill generalized Matthews’ notion of partial metric, in order to establish connections between these structures and the topological aspects of domain theory. Here, we obtain a Banach fixed point theorem for complete partial me...

In this paper we prove a fixed point theorem for six mappings in Menger space using the notion of weakly compatible.

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.

It is shown that if X is a Banach space and C is a union of finitely many nonempty, pairwise disjoint, closed, and connected subsets {Ci : 1≤ i≤ n} of X , and each Ci has the fixed-point property (FPP) for asymptotically regular nonexpansive mappings, then any asymptotically regular nonexpansive self-mapping of C has a fixed point. We also generalize the Goebel-Schöneberg theorem to some Banach...

In this paper, we have given a unique common fixed point theorem for four mappings in a cone metric type space which is a slight variant of theorems of [1, 10]. We also gave an example to illustrate our main theorem. Finally we have given an example in which theorem of [10] is not applicable whereas our corollary is applicable.

In this paper, we prove a common fixed point theorem for single-valued and multivalued mappings on a metric space using the minimal type commutativity condition. We show that continuity of any mapping is not necessary for the existence of a common fixed point.

Recently, the intuitionistic fuzzy stability of Jensen-type functional equation was proved. In this note, we show the intuitionistic fuzzy stability of the Jensen-type functional equation by using the fixed point alternative.