Iterative Approximation of Fixed Points of Almost Contractions

Berinde, Vasile; Pačurar, Mădălina

doi:10.1109/synasc.2007.49

Cited by 335 publications

(404 citation statements)

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“…The standard Picard iteration is used in the Banach Fixed Point Theorem [5] to obtain the existence of the fixed point x * such that x * = w(x * ). The approximation of this point is obtained under additional assumptions on the space X that it should be a Banach one and the mapping w should be contractive.…”

Section: Biomorphs Via Different Types Of Iterationsmentioning

confidence: 99%

Biomorphs via modified iterations

Gdawiec¹,

Kotarski²,

Lisowska³

2016

J. Nonlinear Sci. Appl.

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The aim of this paper is to present some modifications of the biomorphs generation algorithm introduced by Pickover in 1986. A biomorph stands for biological morphologies. It is obtained by a modified Julia set generation algorithm. The biomorph algorithm can be used in the creation of diverse and complicated forms resembling invertebrate organisms. In this paper the modifications of the biomorph algorithm in two directions are proposed. The first one uses different types of iterations (Picard, Mann, Ishikawa). The second one uses a sequence of parameters instead of one fixed parameter used in the original biomorph algorithm. Biomorphs generated by the modified algorithm are essentially different in comparison to those obtained by the standard biomorph algorithm, i.e., the algorithm with Picard iteration and one fixed constant.

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Section: Biomorphs Via Different Types Of Iterationsmentioning

confidence: 99%

Biomorphs via modified iterations

Gdawiec¹,

Kotarski²,

Lisowska³

2016

J. Nonlinear Sci. Appl.

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“…The strong convergence of the net {x t } for a self or nonself nonexpansive singlevalued map T has been investigated by Browder [3], Halpern [7], Jung and Kim [11], Kim and Takahashi [12], Reich [19], Singh and Watson [22], Takahashi and Kim [24], Xu [27], Xu and Yin [29], etc. For details on iterative methods, we refer to [2].…”

Section: Let D Be a Nonempty Closed Convex Subset Of A Banach Space Ementioning

confidence: 99%

Strong convergence results for nonself multimaps in Banach spaces

Shahzad¹,

Zegeye

2007

Proc. Amer. Math. Soc.

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“…It is well known that almost all contractive-type mappings are Picard operators on complete metric spaces. (See for more details [2][3][4][5][6]). …”

Section: Introductionmentioning

confidence: 99%