Strong convergence theorem for strict pseudo-contractions in Hilbert spaces

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2016

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Springeropen

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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In this paper, inspired by Hussain et al. (Fixed Point Theory Appl. 2015: 17, 2015), we study a modified Mann method to approximate strongly fixed points of strict pseudo-contractive mappings. In (Hussain et al. in Fixed Point Theory Appl. 2015: 17, 2015) it is shown that the same algorithm converges strongly to a fixed point of a nonexpansive mapping under suitable hypotheses on the coefficients. Here the assumptions on the coefficients are different, as well as the techniques of the proof.

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KARAPINAR, ERDAL/0000-0002-6798-3254; marino, giuseppe/0000-0001-9381-9338
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KARAPINAR, ERDAL ORCID logo
marino, giuseppe ORCID logo

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Mann's iterations, strict pseudo-contractions mappings, variational inequalities, Mainge's lemma

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31

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https://doi.org/10.1186/s13660-016-1072-6
 https://hdl.handle.net/20.500.14411/510

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