Applications of Hilbert’s projective metric to a class of positive nonlinear operators
✍ Scribed by Min-Jei Huang; Chao-Ya Huang; Tzong-Mo Tsai
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 124 KB
- Volume
- 413
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
If H is a real Hilbert space, K is a closed, generating cone therein and P K is the metric projection onto K; then the following two conditions 1 and 2 are equivalent: 1. (i) P K is isotone: y À xAK ) P K ðyÞ À P K ðxÞAK and (
We present necessary and sufficient conditions for the existence of a positive solution to the system of adjointable operator equations We also derive a representation for a general positive solution to this system when the solvability conditions are satisfied. The results of this paper extend some
In this paper, we study a class of nonlinear operator equations with more extensive conditions in ordered Banach spaces. By using the cone theory and Banach contraction mapping principle, the existence and uniqueness of solutions for such equations are investigated without demanding the existence of