In this chapter, some conclusions are extended to the real Banach space under different mappings, and a proof on the equivalence of Mann and Ishikawa iterative processes with errors under the uniformly pseudo-contractive mapping is given.
In this paper,we establish the equivalence between the convergence of Mann iteration with errors with the convergence of Ishikawa iteration with errors,where T is an uniformly continuous strongly pseudo-contractive mapping.
The purpose of this paper is to study the convergence problem of Ishikawa and Mann iterative processes for a strongly pseudo-contractive mapping T without the Lipschitz condition by using a new approximation method.
A convergence theorem of the Ishikawa iteration sequence with errors for two multivalued strongly pseudo-contractive mappings is given by using an approximation method in real uniformly smooth Banach spaces.
Approximation of fixed points of strictly pseudo-contractive mapping without Lipschitz assumption
In this paper, the iterative approximation of the solution of nonlinear equation Tx=y is given and the iterative approximation of a fixed point of a locally Lipschitzian and strictly pseudo-contractive mapping is discussed.
Let Ubea pseudo-contractive mapping of G into X such that U maps the boundary of B into B.
Using the new analysis techniques, the problem of iterative approximation of solutions of the equation for Lipschitz Φ-strongly accretive operators and of fixed points for Lipschitz Φ-strongly pseudo-contractive mappings are discussed.
Using the new analysis techniques, the problem of iterative approximation of solutions of the equation for Lipschitz ?-strongly accretive operators and of fixed points for Lipschitz ?-strongly pseudo-contractive mappings are discussed.
This paper, presents fixed point theorems on quasi-nonexpansive mappings and pseudo-contractive mappings with boundary conditions in locally convex spaces.
A new class of globally convergent iterations is constructed for the equa- tions of Lipschitzian monotonic mappings on unbounded set in Hilbert space.The iterative processes don't depend upon the Lipschitzian constants of the mappings and converge to a solution which is the nearest to an arbitrarily appointed point in advance among the solutions of the equations.There results have direct ap- plications to pseudo-contractive mappings and linear semi-positive definite mappings.