The purpose of this paper is to establish fixed point results for a single mapping in a partially ordered modular metric space, and to prove a common fixed point theorem for two self-maps satisfying some weak contractive inequalities.

We introduce and study the class of linearly rigid metric spaces; these are the spaces that admit a unique, up to isometry, linearly dense isometric embedding into a Banach space. The first nontrivial example of such a space was given by R. Holmes; he proved that the universal Urysohn space has this property. We give a criterion of linear rigidity of a metric space, which allows us to give a si...

Machine-learning solutions to classification, clustering and matching problems critically depend on the adopted metric, which in the past was selected heuristically. In the last decade, it has been demonstrated that an appropriate metric can be learnt from data, resulting in superior performance as compared with traditional metrics. This has recently stimulated a considerable interest in the to...

the purpose of this paper is to obtain necessary and suffcient conditionsfor existence approximate fixed point on geraghty-contraction. in this paper,denitions of approximate -pair fixed point for two maps tα , sα and theirdiameters are given in a metric space.

This paper studies space bounded algorithms, i.e., algorithms that use a constant amount of scratch space, for the k{server problem. The paper rst shows a characterization of the set of space bounded algorithms that are competitive in nite metric spaces. The result yields a method for (1) e ectively deciding if a given space bounded algorithm is competitive in a given nite metric space, and (2)...