We show how bounds on asymptotic regularity for nonexpansive functions can effectively be converted into certain bounds on the convergence towards a fixed point.

A Smarandache multi-space is a union of n spaces A 1 , A 2 , · · · , A n with some additional conditions holding. Combining Smarandache multi-spaces with classical metric spaces, the conception of multi-metric space is introduced. Some characteristics of a multi-metric space are obtained and Banach's fixed-point theorem is generalized in this paper.

The aim of this paper is to prove a coupled fixed point theorem for a pair of mappings in complex valued metric space, which generalized the results of Marwan Amin Kutbi et al. [4] General Terms: 47H10, 54H25

We give short new geometric proofs of theorems of Bogley and Pride and of Serre. Both follow quickly from a global fixed point theorem. The Bogley–Pride theorem concerns aspherical relative group presentations and was applied in [5] to the multivariable adjunction problem. Serre’s theorem is a basic result concerning group cohomology and finite subgroups.

A hereditarily indecomposable tree-like continuum without the fixed point property is constructed. The example answers a question of Knaster and Bellamy.

Radial lines, suitably parameterized, are geodesics, but notice that the distance from the origin to the (Euclidean) unit sphere is infinite. This model makes it intuitively clear that the boundary at infinity of hyperbolic space is Sn−1. Hyperbolic space together with its boundary at infinity has the topology of a closed ball, and isometries of hyperbolic space extend uniquely to a homeomorphi...

By using the fixed-point index theory and Leggett-Williams fixed-point theorem,we study the existence of multiple solutions to the three-point boundary value problem u′′′ t a t f t, u t , u′ t 0, 0 < t < 1; u 0 u′ 0 0; u′ 1 − αu′ η λ, where η ∈ 0, 1/2 , α ∈ 1/2η, 1/η are constants, λ ∈ 0,∞ is a parameter, and a, f are given functions. New existence theorems are obtained, which extend and comple...

In this paper, we obtain a fixed point theorem for weakly compatible mappings by altering distances between the points via  contractive condition in D-metric spaces. Our work include the results of Bansal, Chugh and Kumar [1], Veerapandi and Chandersekher Rao [14], and Dhage [4]. An example is given at the end to prove the validity of the theorem.

In this paper, we use the concept of a w-distance to prove a common coupled fixed point theorem for a family of maps on a metric space. Our results unify, generalize and complement the comparable results from the current literature.

The main result of this paper is that every non-reflexive subspace Y of L 1 [0, 1] fails the fixed point property for closed, bounded, convex subsets C of Y and nonexpansive (or contractive) mappings on C. Combined with a theorem of Maurey we get that for subspaces Y of L 1 [0, 1], Y is reflexive if and only if Y has the fixed point property. For general Banach spaces the question as to whether...