• Korean Journal of Mathematics
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• v.27 no.4
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• pp.929-947
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• 2019

In the present paper, we investigate the convergence, equivalence of convergence, rate of convergence and data dependence results using a three step iteration process for mappings satisfying certain contractive condition in hyperbolic spaces. Also we give nontrivial examples for the rate of convergence and data dependence results to show effciency of three step iteration process. The results obtained in this paper may be interpreted as a refinement and improvement of the previously known results.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.575-583
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• 2016

In this paper, we study the modified S-iteration process for asymptotic pointwise nonexpansive mappings in a uniformly convex hyperbolic metric space. We then prove the convergence of the sequence generated by the modified S-iteration process.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.869-885
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• 2021

In this article, we define Picard's three-step iteration process for the approximation of fixed points of Zamfirescu operators in an arbitrary Banach space. We prove a convergence result for Zamfirescu operator using the proposed iteration process. Further, we prove that Picard's three-step iteration process is almost T-stable and converges faster than all the known and leading iteration processes. To support our results, we furnish an illustrative numerical example. Finally, we apply the proposed iteration process to approximate the solution of a mixed Volterra-Fredholm functional nonlinear integral equation.

• East Asian mathematical journal
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• v.17 no.2
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• pp.349-365
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• 2001

Let X be a real Banach space and $A:X{\rightarrow}2^X$ be an $\alpha$-strongly accretive operator. It is proved that if the duality mapping J of X satisfies Condition (I) with additional conditions, then the Ishikawa and Mann iteration processes with errors converge strongly to the unique solution of operator equation $z{\in}Ax$. In addition, the convergence of the Ishikawa and Mann iteration processes with errors for $\alpha$-strongly pseudo-contractive operators is given.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.765-773
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• 1998

Let E be a smooth Banach space. Suppose T : E longrightarrow E is a strongly accretive map. It is proved that each of the two well known fixed point iteration methods (the Mann and Ishikawa iteration methods), under suitable conditions, converges strongly to a solution of the equation Tx = f.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.1-14
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• 2024

In this paper, we establish strong and ∆-convergence theorems for new iteration process namely S-R iteration process for a generalized α-nonexpansive mappings in a uniformly convex hyperbolic space and also we show that our iteration process is faster than other iteration processes appear in the current literature's. Our results extend the corresponding results of Ullah et al. [5], Imdad et al. [16] in the setting of uniformly convex hyperbolic spaces and many more in this direction.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.477-485
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• 1997

Let E be a smooth Banach space. Suppose T:$E \rightarrow E$ is a strongly accretive map. It is proved that each of the two well known fixed point iteration methods (the Mann and ishikawa iteration methods), under suitable conditions converges strongly to a solution of the equation $T_x=f$.

• The Pure and Applied Mathematics
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• v.13 no.1 s.31
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• pp.39-46
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• 2006

We establish a general theorem to approximate fixed points of quasicontractive operators on a normed space through the Noor iteration process with errors in the sense of Liu [9]. Our result generalizes and improves upon, among others, the corresponding result of Berinde [1].

• East Asian mathematical journal
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• v.26 no.5
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• pp.693-702
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• 2010

We study one-step iteration process to approximate common fixed points of two nonexpansive mappings and prove some convergence theorems in convex metric spaces. Using the so-called condition (A'), the convergence of iteratively defined sequences in a uniformly convex metric space is also obtained.

• The Pure and Applied Mathematics
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• v.16 no.3
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• pp.307-314
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• 2009

The purpose of this paper is to establish a strong convergence of an implicit iteration process with errors to a common fixed point for a finite family of continuous strongly pseudocontractive mappings. The results presented in this paper extend and improve the corresponding results of References [2, 6, 11-12].