Existence, uniqueness and approximation of a solution for a k-positive definite operator equation

Abstract

The notion of a K-positive definite (Kpd) operator which has been studied for Hilbert spaces is extended to real separable smctly convex Banach spaces, X. For such an X, it is proved that the equation Au = f, f E X, where A is a Kpd operator with the same domain as K, has a unique solution. Furthermore, a strongly convergent interation process is constructed.

Keywords:

• K-positive definite operator
• Fixed Point Iteration process

^*Research was supported by a grant from the TWAS (TWAS RG-88-14), ICTP, Trieste, Italy.

^*Research was supported by a grant from the TWAS (TWAS RG-88-14), ICTP, Trieste, Italy.

Notes

^*Research was supported by a grant from the TWAS (TWAS RG-88-14), ICTP, Trieste, Italy.