k=1 Gk(ω) · 1(uk,vk](s), ω ∈ Ω, s ≥ 0, where n ∈ N, 0 ≤ uk < vk, and Gk ∈ L(Fuk). We let Le denote the class of all such integrands. Notice that each H ∈ Le satisfies (i) s → Hs(ω) is a left-continuous step function for each ω ∈ Ω, (ii) Hs ∈ L(Fs) for each s ≥ 0, (iii) viewed as a mapping from Ω × [0, t] to R, (ω, s) → Hs(ω) is Ft ⊗B[0,t] measurable for each t > 0, and (iv) E[ ∫ t 0 H s ds] < ∞...

In this paper, we prove the existence theorem for a mapping defined by T = T1 + T2 when T1 is a μ1-Lipschitz continuous and γ-strongly monotone mapping, T2 is a μ2-Lipschitz continuous mapping, we have a mapping T is Lipschitz continuous but not strongly monotone mapping. This work is extend and improve the result of N. Petrot [17]. Mathematics Subject Classification: 46C05, 47D03, 47H09, 47H10...

Optical mapping is a novel technique for generating the restriction map of a DNA molecule by observing many single, partially digested copies of it, using fluorescence microscopy. The real-life problem is complicated by numerous factors: false positive and false negative cut observations, inaccurate location measurements, unknown orientations, and faulty molecules. We present an algorithm for s...

We show that if X is a separable Banach space (or more generally a Banach with an infinite-dimensional separable quotient) then there is a continuous mapping f : X → X such that the autonomous differential equation x′ = f(x) has no solution at any point. In order to put our results into context, let us start by formulating the classical theorem of Peano. Theorem 1. (Peano) Let X = R, f : R×X → ...

begin{abstract} in this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable banach space. end{abstract}

This talk is based on work with N. Khuri and H. Ren.[1,2] The main new tools we use are theorems by Voronin on the universality properties of the Riemann Zeta function, ζ(s), in the critical strip, 1 2 < Re s < 1. Given any real continuous function, φ(x), 0 ≤ x ≤ L, we can choose a mapping, s(x), which maps the line, 0 ≤ x ≤ L, onto a line s(x) that lies in the strip 1 2 < Re s < 1, then given ...

In this paper we propose and studied a new composite iterative scheme with certain control con-ditions for viscosity approximation for a zero of accretive operator and xed points problems in areflexive Banach space with weakly continuous duality mapping. Strong convergence of the sequencefxng dened by the new introduced iterative sequence is proved. The main results improve andcomplement the co...

In this work‎, ‎we formulate Chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and‏ ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. We also discuss the uniqueness of the fixed point. The given result is a generalization of Chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a graph.

We study metric spheres ( Z , d ) $(Z, d_{Z} )$ obtained by gluing two hemispheres of S 2 $\mathbb {S}^{2}$ along an orientation-preserving homeomorphism g : 1 → $g \colon \mathbb {S}^{1} \rightarrow {S}^{1}$ where $d_{Z}$ is the canonical distance that locally isometric to off seam. show if quasiconformally equivalent in geometric sense, then $g$ a welding with conformally removable curves. al...