The first part of the present paper is devoted to a systematic construction of continuous-time finite-dimensional integrable systems arising from the rational su(2) Gaudin model through certain contraction procedures. In the second part, we derive an explicit integrable Poisson map discretizing a particular Hamiltonian flow of the rational su(2) Gaudin model. Then, the contraction procedures en...

Boujari [5] proved a fixed point theorem with an old version of the integraltype contraction , his proof is incorrect. In this paper, a new generalizationof integral type contraction is introduced. Moreover, a fixed point theorem isobtained.

Introduction. In this paper we discuss some recent results about maps of complex algebraic varieties. A contraction ϕ : X → Z is a proper surjective map of normal varieties with connected fibers. We will always assume that X, if not smooth, has mild singularities; in particular we assume that a rational multiple of the canonical sheaf, rK X , is a Cartier divisor. In this hypothesis the contrac...

boujari [5] proved a fixed point theorem with an old version of the integraltype contraction , his proof is incorrect. in this paper, a new generalizationof integral type contraction is introduced. moreover, a fixed point theorem isobtained.

A very engrossing technique in theory of contractive mapping fixed point. number authors have defined type mappings on a cone metric spaces X which are generalization the well -known Banach contraction, and property that each such has unique The point can always be found by using Picard Iteration, opening with initial choice x0∈X. In this manuscript, we generalize, extend improve res...

We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contrac...

Abstract We improve the rational contractive condition and prove common fixed point in dislocated metric spaces. In addition, new generalized contraction has existence of a solution for system integral equations.