LetK be a nonempty closed convex subset of a real Banach space E, T : K → K a uniformly L-Lipschitzian asymptotically pseudocontractive mapping with sequence {kn}n≥0 ⊂ [1,∞), lim n→∞ kn = 1 such that p ∈ F (T ) = {x ∈ K : Tx = x}. Let {an}n≥0, {bn}n≥0 , {cn}n≥0 be real sequences in [0, 1] satisfying the following conditions: (i) an + bn + cn = 1; (ii) ∑ n≥0 bn =∞; (iii) cn = o(bn); (iv) lim n→∞...

We consider a broad class of Approximate Message Passing (AMP) algorithms defined as Lipschitzian functional iteration in terms an n×n random symmetric matrix A. establish universality noise for this AMP the n-limit and validate behavior number AMPs popularly adapted compressed sensing, statistical inferences, optimizations spin glasses.

X iv :0 70 5. 35 56 v1 [ m at h. FA ] 2 4 M ay 2 00 7 New Generalization of Perturbed Ostrowski Type Inequalities and Applications Wen-jun Liu, Qiao-ling Xue, Jian-wei Dong Abstract: Generalizations of Ostrowski type inequality for functions of Lipschitzian type are established. Applications in numerical integration and cumulative distribution functions are also given.

We introduce and study a new class of generalized nonlinear implicit quasivariational inclusions involving relaxed Lipschitzian mappings. We prove the existence of solution for the generalized nonlinear implicit quasivariational inclusions and construct some new stable perturbed iterative algorithms with errors. We also give an application to a class of generalized nonlinear implicit variationa...

A convex cone metric space is a cone metric space with a convex structure. In this paper, we extend an Ishikawa type iterative scheme with errors to approximate a common fixed point of two sequences of uniformly quasi-Lipschitzian mappings to convex cone metric spaces. Our result generalizes Theorem 2 in [1].

We deal in this study with the convergence of a class of numerical schemes for scalar conservation laws including stiff source terms. We suppose that the source term is dissipative but it is not necessarily a Lipschitzian function. The convergence of the approximate solution towards the entropy solution is established for first and second order accurate MUSCL and for splitting semi-implicit met...

The purpose of this paper is to introduce a general iterative method for finding solutions of a general system of variational inclusions with Lipschitzian relaxed cocoercive mappings. Strong convergence theorems are established in strictly convex and 2-uniformly smooth Banach spaces. Moreover, we apply our result to the problem of finding a common fixed point of a countable family of strict pse...

This paper studies the variation of the volume of a subanalytic family of sets. More precisely we are interested in the variation of the density. We prove that the density is continuous along a stratum of a Whitney subanalytic stratification and locally lipschitzian when the stratification satisfies the Kuo-Verdier condition. This problem had been studied by Comte in [C].

In this paper, the equivalence of the convergence among Mann-Ishikawa and Noor iterations is obtained for uniformly L-Lipschitzian mappings in real Banach spaces. Our results extend and improve the corresponding results in Chang [3] and Ofoedu [4]. Mathematics subject classification (2010): 47H10, 47H09, 46B20..