Iterative processes with errors for nonlinear equations
Łjubomir Ćirić,Jeong Sheok Ume +1 more
TL;DR: In this article, a class of multi-valued and single-valued operators of generalised monotone type was introduced and a new general lemma on the convergence of real sequences and some new convergence theorems for the Ishikawa and Mann iteration processes with errors to the unique fixed point of such operators were proved.
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Abstract: In this paper we introduce and consider a class of multi-valued and single-valued operators of generalised monotone type We proved a new general lemma on the convergence of real sequences and some new convergence theorems for the Ishikawa and Mann iteration processes with errors to the unique fixed point of such operators, which are not necessarily Lipschitz operators Our results generalise, improve, and extend several recent results
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Citations
On Mann implicit iterations for strongly accretive and strongly pseudo-contractive mappings
TL;DR: This paper studied the Mann implicit iteration sequence for strongly accretive and strongly pseudo-contractive mappings and showed that this implicit scheme gives better convergence rate estimate than the classical Picard-type iteration process.
36
On the steepest descent approximation method for the zeros of generalized accretive operators
TL;DR: In this article, the convergence of the generalized steepest descent approximation process to a zero of a generalized strongly accretive operator, defined on a uniformly smooth Banach space, was studied.
21
Modified ishikawa iteration process for nonlinear lipschitz generalized strongly pseudo-contractive operators in arbitrary banach spaces
TL;DR: In this paper, the Ishikawa iteration process was modified to be associated with a nonlinear Lipschitzian generalized strongly pseudo-contractive operator with a fixed point in a (not necessarily uniformly smooth) Banach space.
9
The convergence of an implicit mean value iteration
TL;DR: It is shown that the convergence of an implicit mean value iteration when applied to uniformly pseudocontractive maps is the same as when it was shown in the previous chapter.
Stability and convergence of a new composite implicit iterative sequence in Banach spaces
Liping Yang,Weiming Kong +1 more
TL;DR: In this paper, a composite implicit iteration process in an arbitrary real Banach space was proposed to study stability and strong convergence of pseudocontractive mappings by using a new composite implicit iterative process.
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Iterative Solution of Nonlinear Equations of the Φ-Strongly Accretive Type
TL;DR: In this paper, it was proved that under suitable conditions on the real sequences {αn}n = 0∞ and {βn} n=0∞, the iteration process converges strongly to the unique solution of the equationTx=f.
108