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Stability of Mann and Ishikawa Iterative TechniquesOnly 14 pages are availabe for public view
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Abstract
During the last two decades, the problem of constructing iterative
techniques for solving different nonlinear problems tackled the ingenuity
of many researchers, and has the greatest interest of many of the recent
research papers.
The main objective of the present thesis is to construct the proofs
of many convergence theorems associated with applying the recent
iterative techniques to solve the most general nonlinear operator equation
of the form A.:\”+ ...t Tx =f in the most general functional spaces.
In this research, trials are made to investigate the convergence of
the Mann and Ishikawa iterative processes with errors to the unique
solution of the general nonlinear operator equation, mentioned before, in
Banach space where A, T: X -+ X are Lipschitzian, A is strongly accretive
and T is accretive.
Furthermore, with some modifications in the proofs of the
convergence theorems. fixed point approximations for strongly
pseudocontractivc operators arc: also studied.
Since the class of ¢-strongly accretive operators is more general
than that of accretive operators, then convergence theorems for this class
of operators are introduced.
Finally, new results concerning T-stability of the Mann and
Ishikawa iterations with errors with respect to Lipschitzian mappings in a
general complex Banach space have been established