Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semicontractive) systems, the distance semidistance) between any two trajectories decreases exponentially fast. partially each trajectory converges fast to an invariant subspace. In this article, we develop contraction Hilbert spaces. First, provide a novel integral condition contractivity, ...

In this paper, some results of the Chebyshev type integral inequality for the pseudo-integral are proven. The obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. Finally, we applied our results  to the case of comonotone functions.

Maintenance of metabolic alkalosis generated by chloride depletion is often attributed to volume contraction. In balance and clearance studies in rats and humans, we showed that chloride repletion in the face of persisting alkali loading, volume contraction, and potassium and sodium depletion completely corrects alkalosis by a renal mechanism. Nephron segment studies strongly suggest the correc...

background: the vascular function of angiotensin ii-type-2 receptors in adults is controversial. we sought their location and function in mouse aortic rings at young and old mice. materials and methods: male c57bl mice (aged 4 and 14 months) were killed by co2. the descending thoracic aorta was cleaned and dissected into rings. aortic rings were mounted in krebs’ solution at 37 °c and then setu...

These notes contain various versions of the contraction mapping principle. Several applications to existence theorems in the theories of differential and integral equations and variational inequalities are given. Also discussed are Hilbert’s projective metric and iterated function systems

We have investigated the existence and uniqueness solutions of the nonlinear fractional differential equation of an arbitrary order with integral boundary condition. The result is an application of the Schauder fixed point theorem and the Banach contraction principle.

The purpose of this paper is to present some new contraction mappings via control functions. In addition, fixed point results for Θ,α,θ,Ψ contraction, rational and almost are obtained. Moreover, under types (I), (II), (III) Θ,θ,Ψυ0, several circle solutions provided in the setting a G-Metric space. Our extend, unify, generalize many previously published papers direction. examples show reliabili...

In this article, we extend fractional operators with nonsingular Mittag-Leffler kernels, a study initiated recently by Atangana and Baleanu, from order [Formula: see text] to higher arbitrary order and we formulate their correspondent integral operators. We prove existence and uniqueness theorems for the Caputo ([Formula: see text]) and Riemann ([Formula: see text]) type initial value problems ...

As other authors have been very interested in the topic of fixed points, we obtained some results this study that emphasize importance point theory. Kannan described a more general contraction than Banach took its name and later Reich generalized further metric spaces. In paper, introduced new contractions called type γ-contraction which are generalization for non-Archimedean fuzzy We presented...