Well-posedness via Monotonicity. An Overview

The idea of monotonicity (or positive-definiteness in the linear case) is shown to be the central theme of the solution theories associated with problems of mathematical physics. A "grand unified" setting is surveyed covering a comprehensive class of such problems. We elaborate the applicability of our scheme with a number examples. A brief discussion of stability and homogenization issues is also provided.Comment: Thoroughly revised version. Examples correcte

On the homogenization of partial integro-differential-algebraic equations

We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics, elasticity, electro-magnetism and coupled systems thereof. The approach permits the consideration of memory problems as well as differential-algebraic equations. We show that the limit equation is well-posed and causal. We rely on techniques from functional analysis and operator theory only.Comment: Thoroughly revised, changed title, reviewer's comments incorporated, added some references. 41 page

Data dependence results of a new multistep and S-iterative schemes for contractive-like operators

In this paper, we prove that convergence of a new iteration and S-iteration can be used to approximate to the fixed points of contractive-like operators. We also prove some data dependence results of this new iteration and S-iteration schemes for contractive-like operators. Our results extend and improve some known results in the literature.Comment: arXiv admin note: text overlap with arXiv:1211.570

Teoreme de punct fix pentru operatori multivoci contractivi in spatii metrice generalizate

In this paper we give a xed point results for multivalued operators on generalized metric spaces endowed with a generalized w-distance. Then we study the data dependence for this new result.multivalued weakly Picard operator, w-distance, fxed point, multivalued operator