in this paper is introduced a new type of generalization of metric spaces called sb metric space. for this new kind of spaces it has been proved a common xed point theorem for four mappings which satisfy generalized contractive condition. we also present example to conrm our theorem.

An approach to weak balance laws in Continuum Mechanics is presented, involving densities with only divergence measure, which relies on the balance of power. An equivalence theorem between Cauchy powers and Cauchy fluxes is proved. As an application of this method, the construction of the stress tensor when the body is an orientable differential manifold is achieved under very general assumptions.

Abstract. Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic properties of the spectral densities of these random fields are studied. The associated self-similar random fields obtained by applying the Lamperti transf...

In this paper we study the concepts of I-Cauchy and I∗-Cauchy for double sequences in a linear metric space. Also, we give the relation between I-convergence and I∗-convergence of double sequences of functions defined between linear metric spaces.

In this note a singular abstract Cauchy problem is considered. A solution is obtained for this problem in terms of a regular abstract Cauchy problem. As an application we obtain a new solution of the initial value problem for a class of singular partial differential equations.

The (Cauchy) initial value formulation of General Relativity is developed, and the maximal vacuum Cauchy development theorem is reviewed. There is a short discussion of the evolution equations and associated guage choices, and global results are mentioned briefly in the conclusion.

In this series of articles we study connections between combinatorics of multidimensional generalizations of Cauchy identity and continuous objects such as multidimensional Brownian motions and Brownian bridges. In Part I of the series we present a bijective proof of multidimensional generalizations of the Cauchy identity. Our bijection uses oriented planar trees equipped with some linear orders.

Part I: Single Variables: Review and extensions. CR equations and analyticity; Cauchy-Goursat theorem and Cauchy integral formula, Louiville’s theorem; Morera’s theorem; maximum modulus principle; Laurent series and singularities; Riemann extension theorem; residues; Schwartz’s lemma; open mapping theorem; analytic continuation and the dilogarithm; linear fractional transformations; spaces of a...

We study many properties of Cauchy numbers in terms of generating functions and Riordan arrays and find several new identities relating these numbers with Stirling, Bernoulli and harmonic numbers. We also reconsider the Laplace summation formula showing some applications involving the Cauchy numbers.