𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the Semi-monotone Operator Theory and Applications

✍ Scribed by Yu-Qing Chen

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
112 KB
Volume
231
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, E is a real Banach space, A : E** = E** ª E* is a semi-monotone operator. We first study the variational inequality problem: Find u g K, such Ž Ž . . that A u, u , ¨y u G 0, where K ; E** is a closed convex subset; then the Ž . operator equation A u, u s p*, and we also construct a degree theory for demicontinuous semi-monotone operators in reflexive Banach spaces.

📜 SIMILAR VOLUMES

On the Monotonicity of Positive Linear O
On the Monotonicity of Positive Linear Operators
✍ M.Kazim Khan; B. Della Vecchia; A. Fassih 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 377 KB

We provide sufficient conditions for a sequence of positive linear approximation operators, L n ( f, x), converging to f (x) from above to imply the convexity of f. We show that, for the convolution operators of Feller type, K n ( f, x), generated by a sequence of iid random variables taking values

Consistency of iterative operator-splitt
Consistency of iterative operator-splitting methods: Theory and applications
✍ Jürgen Geiser 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 295 KB

## Abstract In this article, we describe a different operator‐splitting method for decoupling complex equations with multidimensional and multiphysical processes for applications for porous media and phase‐transitions. We introduce different operator‐splitting methods with respect to their usabilit

New Fixed Point Theorems of Mixed Monoto
New Fixed Point Theorems of Mixed Monotone Operators and Applications
✍ Zhang Zhitao 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 161 KB

In this paper, a class of mixed monotone operators with convexity and concavity are investigated, and existence and uniqueness theorems of fixed points are obtained. Moreover, some applications to nonlinear integral equations on unbounded regions and differential equations in Banach spaces are given

On the Property of Monotonic Convergence
On the Property of Monotonic Convergence for Beta Operators
✍ José A. Adell; F. Germán Badı́a; Jesús de la Cal; Fernando Plo 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 329 KB

We show that beta operators satisfy the property of monotonic convergence under convexity. This gives a positive answer to a question recently posed by M. K. Khan. Some additional properties, consequences and applications are also discussed. Throughout this paper, probabilistic methods play a fundam