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Fractals via Ishikawa Iteration
, 2011Fractal geometry is an exciting area of interest with diverse applications in various disciplines of engineering and applied sciences. There is a plethora of papers on its versatility in the literature. The basic aim of this paper is to study the pattern of attractors of the iterated function systems (IFS) through Ishikawa iterative scheme.
B. Prasad, Kuldip Katiyar
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Mathematical methods in the applied sciences, 2023
In this article, an Ishikawa iteration scheme is modified for b$$ b $$ ‐enriched nonexpansive mapping to solve a fixed point problem and a split variational inclusion problem in real Hilbert spaces.
P. Phairatchatniyom +2 more
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In this article, an Ishikawa iteration scheme is modified for b$$ b $$ ‐enriched nonexpansive mapping to solve a fixed point problem and a split variational inclusion problem in real Hilbert spaces.
P. Phairatchatniyom +2 more
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The equivalence between Mann–Ishikawa iterations and multistep iteration
Nonlinear Analysis: Theory, Methods & Applications, 2004In this interesting paper, the authors consider the equivalence between the one-step, two-step, three-step and multistep-iteration process for solving the nonlinear operator equations \(Tu = 0\) in a Banach space for pseudocontractive operators \(T\). It is worth mentioning that three-step iterative schemes were introduced by \textit{M. A.
Rhoades, B. E., Soltuz, Stefan M.
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Fixed point approximation under Mann iteration beyond Ishikawa
Commentationes Mathematicae Universitatis Carolinae, 2020Summary: Consider the Mann iteration \(x_{n+1}=(1-\alpha_n)x_n+\alpha_nTx_n\) for a nonexpansive mapping \(T\colon K\to K\) defined on some subset \(K\) of the normed space \(X\). We present an innovative proof of the Ishikawa almost fixed point principle for nonexpansive mapping that reveals deeper aspects of the behavior of the process.
Hester, Anthony, Morales, Claudio H.
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Random Ishikawa Iterative Sequence with Applications
Stochastic Analysis and Applications, 2005The purpose of this paper is to construct a random Ishikawa iterative sequence for random strongly pseudo-contractive operator T in separable Banach spaces and to study that under suitable conditions this random iterative sequence converges to a random fixed point to T.
S.S. Chang +3 more
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Convergence of Ishikawa’s iteration method for pseudocontractive mappings
Nonlinear Analysis: Theory, Methods & Applications, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zegeye, Habtu +2 more
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Remark on stability of Ishikawa iterative procedures
Applied Mathematics and Mechanics, 2002In this paper, the authors consider the stability of the two-step (Ishikawa) iterations for solving nonlinear equations in a Banach spaces. The results proved in this paper improve and refine the previously known results. Essentially using the technique developed in this paper, one can study the stability of the three-step iterations (known as Noor ...
Xue, Zhiqun, Tian, Hong
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Ishikawa Iterative Process in Uniformly Smooth Banach Spaces
Applied Mathematics and Mechanics, 2001This article deals with Ishikawa approximations \[ x_{n+1}= (1-\alpha_n) x_n+ \alpha_nTy_n,\;y_n=(1-\beta_n)x_n+\beta_nTx_n\;(n=1,2,\dots) \] for a continuous \(\Phi\)-strongly pseudocontractive operator \(T:K\to K\) (this means that for the duality mapping \(J\) and a strictly increasing function \(\varphi:[0,\infty) \to[0 ,\infty)\), \(\varphi(0) =0\)
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