In this paper first we prove a common fixed point theorem in Menger probabilistic metric spaces. Then we present a nonlinear contraction case of Jungck’s common fixed point theorem in Menger probabilistic metric spaces. Finally, we prove a common fixed point theorem for six self-maps in a Menger probabilistic metric space. 2007 Elsevier Inc. All rights reserved.

The edge-contraction axioms are introduced for topological recursion of multilinear maps that arise from cellular graphs, and it is proven that these axioms are equivalent to topological quantum field theories over a Frobenius algebra, assuming the consistency of the axioms. As an example, the concrete formulas of topological quantum field theories on the finite-dimensional abelian group algebr...

Results on common fixed points for pairs of single and multivalued mappings on a complete metric space are examined. Our work establishes a common fixed point theorem for a pair of generalized contraction self-maps and a pair of set-valued mappings.

A recent nonlinear alternative for contraction maps in Fréchet spaces due to Frigon and Granas is used to investigate the existence and uniqueness of solutions to first-order boundary value problems for impulsive functional differential equations with infinite delay. An example to illustrate the results is included.

By introducing a new concept called “set-valued asymptotic contraction of final type” in metric spaces, the existence and uniqueness of compact fixed sets for such mappings have been obtained. Furthermore, by adding additional conditions, we prove the existence and uniqueness of endpoints for these maps. 2010 Mathematics Subject Classification: 47H10; 54C60

The intent of the paper is to study semi-cyclic type contraction condition for a pair of maps (S, T). Our aim is to establish an existence theorem for common fixed points and best proximity points for such a pair in Banach spaces. The results obtained herein extend some recent results.

In this paper, we study some tripled fixed and coincidence point theorems for two mappings F : X×X×X → X and g : X → X satisfying a nonlinear contraction based on φ-maps. Our results extend and improve many existing results in the literature. Also, we introduce an example to support the validity of our results.

We introduce the measurement idea in domain theory and then apply it to establish two fixed point theorems. The first is an extension of the Scott fixed point theorem which applies to nonmonotonic mappings. The second is a contraction principle for monotone maps that guarantees the existence of unique fixed points.

Hierarchical representations, such as irregular pyramids, are the bases of several applications in the field of discrete imagery. So, ndimensional ”bottom-up” irregular pyramids can be defined as stacks of successively reduced n-dimensional generalized maps (n-G-maps) [11], each n-G-map being defined from the previous level by using removal and contraction operations defined in [8]. Our goal is...

In this paper we consider practical stabilization strategies of scalar linear systems by means of quantized feedback maps which use a minimal number of quantization levels. These stabilization schemes are based on the chaotic properties of piecewise affine maps and their performance can be analyzed in terms of the mean time needed to shrink the system from an initial interval into a fixed targe...