We consider a stochastic nonlinear fractional Langevin equation of two orders Dβ(Dα+γ)ψ(t)=λϑ(t,ψ(t))w˙(t),0<t≤1. Given some suitable conditions on the above parameters, we prove existence and uniqueness mild solution to initial value problem for using Banach fixed-point theorem (Contraction mapping theorem). The upper bound estimate second moment is given, which shows exponential growth in ...

Introduction: The 12-lead electrocardiogram (ECG) is the most widely-used tool for the detection and diagnosis of cardiac conditions including myocardial infarction and ischemia. It has therefore been a focus of cardiac modeling. However, the most contemporary in silico ECG investigations of the intact heart have assumed a static heart and ignored the mechanical contraction that is an essential...

We develop a dilation theory for row contractions T := [T1, . . . , Tn] subject to constraints such as p(T1, . . . , Tn) = 0, p ∈ P , where P is a set of noncommutative polynomials. The model n-tuple is the universal row contraction [B1, . . . , Bn] satisfying the same constraints as T , which turns out to be, in a certain sense, the maximal constrained piece of the n-tuple [S1, . . . , Sn] of ...

‎In this paper, based on [A. Razani, V. Rako$check{c}$evi$acute{c}$ and Z. Goodarzi, Nonself mappings in modular spaces and common fixed point theorems, Cent. Eur. J. Math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $T$ in the modular space $X_rho$ is presented. Moreover, we study a new version of Krasnoseleskii's fixed point theorem for $S+T$, where $T$ is a cont...

In this paper, we consider the second-order nonlinear and the nonlinear neutral functional differential equations (a(t)x′(t))′ + f(t, x(g(t))) = 0, t ≥ t0 (a(t)(x(t)− p(t)x(t− τ))′)′ + f(t, x(g(t))) = 0, t ≥ t0 . Using the Banach contraction mapping principle, we obtain the existence of throughout positive solutions for the above equations.

Meir and Keeler in 1 considered an extension of the classical Banach contraction theorem on a complete metric space. Kirk et al. in 2 extended the Banach contraction theorem for a class of mappings satisfying cyclical contractive conditions. Eldred and Veeramani in 3 introduced the following definition. Let A and B be nonempty subsets of a metric space X. A map T : A ∪ B → A ∪ B, is a cyclic co...

in this paper, we establish and prove the existence of best proximity points for multivalued cyclic $f$- contraction mappings in complete metric spaces. our results improve and extend various results in literature.

recently, choudhury and metiya [fixed points of weak contractions in cone metric spaces, nonlinear analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. weak contractions are generalizations of the banach's contraction mapping, which have been studied by several authors. in this paper, we introduce the notion of $f$-weak contractions and als...

Let (X , d) be a complete metric space, m ∈ N \ {0}, and γ ∈ R with 0 ≤ γ < 1. A g-contraction is a mapping T : X −→ X such that for all x, y ∈ X there is an i ∈ [1,m] with d(T ix,T iy) <R γid(x, y). The generalized Banach contractions principle states that each g-contraction has a fixed point. We show that this principle is a consequence of Ramsey’s theorem for pairs over, roughly, RCA0 + Σ2-I...

We construct a family of $q$ deformations $E(2)$ group for nonzero complex parameters $|q|<1$ as locally compact braided quantum groups over the circle $\mathbb{T}$ viewed quasitriangular with respect to unitary R-matrix $R(m,n):=(\zeta)^{mn}$ all $m,n\in\mathbb{Z}$. For real $0<|q|<1$, deformation coincides Woronowicz's $E_{q}(2)$ groups. As an application, we study analogue contraction proced...