On solving Lipschitz pseudocontractive operator equations

On Convergence Results for Lipschitz Pseudocontractive Mappings

Adaptive Mann iterations for nonlinear accretive and pseudocontractive operator equations

We construct adaptive Mann iterations for finding fixed points of strongly pseudocontractive mappings and solving nonlinear strongly accretive (not necessary continuous) operator equation Sx = f in p-smooth Banach spaces.

On the Lipschitz Operator Algebras

In a recent paper by H. X. Cao, J. H. Zhang and Z. B. Xu an α-Lipschitz operator from a compact metric space into a Banach space A is defined and characterized in a natural way in the sence that F : K → A is a α-Lipschitz operator if and only if for each σ ∈ X∗ the mapping σ ◦ F is a α-Lipschitz function. The Lipschitz operators algebras Lα(K,A) and lα(K,A) are developed here further, and we st...

On fully operator Lipschitz functions

Let A(D) be the disc algebra of all continuous complex-valued functions on the unit disc D holomorphic in its interior. Functions from A(D) act on the set of all contraction operators (‖A‖ 1) on Hilbert spaces. It is proved that the following classes of functions from A(D) coincide: (1) the class of operator Lipschitz functions on the unit circle T; (2) the class of operator Lipschitz functions...

‎A matrix LSQR algorithm for solving constrained linear operator equations

In this work‎, ‎an iterative method based on a matrix form of LSQR algorithm is constructed for solving the linear operator equation $mathcal{A}(X)=B$‎ ‎and the minimum Frobenius norm residual problem $||mathcal{A}(X)-B||_F$‎ ‎where $Xin mathcal{S}:={Xin textsf{R}^{ntimes n}~|~X=mathcal{G}(X)}$‎, ‎$mathcal{F}$ is the linear operator from $textsf{R}^{ntimes n}$ onto $textsf{R}^{rtimes s}$‎, ‎$ma...