A discrete time tâtonnement process is presented for reaching an equilibrium of an exchange economy. The process is based on updating the prices in proportion to excess demands of the commodities such that the new prices are positive and their changes are bounded. Global convergence conditions for the process are given and convergence is shown when the excess demand function has the gross subst...

In this paper, we prove strong convergence results for a modified Mann iterative process for a new class of I- nearly weak uniformly L-Lipschitzian mappings in a real Banach space. The class of I-nearly weak uniformly L-Lipschitzian mappings is an interesting generalization of the class of nearly weak uniformly L-Lipschitzian mappings which inturn is a generalization of the class of nearly unif...

We introduce a low-order stabilized discretization of the primitive equations of the ocean with highly reduced computational complexity. We prove stability through a specific inf–sup condition, and weak convergence to a weak solution. We also perform some numerical tests for relevant flows. © 2012 Elsevier Ltd. All rights reserved.

In this paper, we prove the weak convergence of a modified Khan iteration for nonself I nonexpansive mapping in a Banach space which satisfies Opial’s condition. Our result extends and improves these announced by S. Chornphrom and S.Phonin [Weak Converges Theorem of Noor iterative Scheme for Nonself I-Nonexpansive mapping, Thai Journal of Mathematics Volume 7(2009) no.2:311-317].

Under the hypothesis that the derivative satisfies some kind of weak Lipschitz condition, sharp estimates of the radii of convergence balls of Newton-like methods for operator equations are given in Banach space. New results can be used to analyze the convergence of other developed Newton iterative methods.