On the approximation of solutions to a fixed point problem with inequality constraints in a Banach space partially ordered by a cone

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2017

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Springer Singapore

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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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Let E be a Banach space with a cone P. Let T, ϕi: E → E (i = 1, 2) be three given operators. We address the following question: Find x ε E such that where ≤P is the partial order on E induced by the cone P, and 0E is the zero vector of E. We obtain sufficient conditions for the existence and uniqueness of solutions to this problem. We present an iterative algorithm to approximate the solution. The error estimates as well as results concerning the data dependence, well-posedness, limit shadowing property, and sequences of operators are provided. Some interesting consequences are deduced from our main results. © Springer Nature Singapore Pte Ltd. 2017. All rights reserved.

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Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness

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441

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455

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https://doi.org/10.1007/978-981-10-3722-1_12
 https://hdl.handle.net/20.500.14411/3860

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Scopus