It is often demonstrated that Brouwer’s fixed point theorem can not be constructively proved. Therefore, Kakutani’s fixed point theorem, the Fan-Glicksberg fixed point theorem and the existence of a pure strategy Nash equilibrium in a strategic game with continuous (infinite) strategies and quasi-concave payoff functions also can not be constructively proved. On the other hand, however, Sperner...

We introduce the concept of (EA) property and occasional w-compatibility for hybrid pair F : X × X → 2 (X) and f : X → X. We also introduce common (EA) property for two hybrid pairs F, G : X → 2 (X) and f, g : X → X. We establish some common coupled fixed point theorems for two hybrid pairs of mappings under φ-ψ contraction on noncomplete metric spaces. An example is also given to validate our ...

this paper presents some results concerning the existence of solutions for a functional integral equation of volterra type in two variables, via measure of noncompactness. two examples are included to illustrate the main result.

In this paper, sufficient conditions for the existence of common fixed points for a compatible pair of self maps of Gregustype in the framework of convex metric spaces have been obtained. Also, established the existence of common fixed points for a pair of compatible mappings of type (B) and consequently for compatible mappings of type (A). The proved results generalize and extend some of the w...

Abstract. We define the infinite dimensional simplex to be the closure of the convex hull of the standard basis vectors in R∞, and prove that this space has the fixed point property: any continuous function from the space into itself has a fixed point. Our proof is constructive, in the sense that it can be used to find an approximate fixed point; the proof relies on elementary analysis and Sper...

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.

Here we generalise, improve and unify the fixed point theorems due to Delbosco[1], Skof[8], Khan et al.[5] and several other fixed point theorems for a single map and common fixed point theorems ([6], [7]) for a pair of mappings in a setting of 2-metric space. 2000 Mathematics Subject Classification: 47H10, 54H25.

Here we generalise, improve and unify the fixed point theorems due to Delbosco[1], Skof[8], Khan et al.[5] and several other fixed point theorems for a single map and common fixed point theorems ([6], [7]) for a pair of mappings in a setting of 2-metric space. 2000 Mathematics Subject Classification: 47H10, 54H25.