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Matematicheskie Zametki, 2021, Volume 110, Issue 4, paper published in the English version journal (Mi mzm13304)  
This article is cited in 1 scientific paper (total in 1 paper)

Papers published in the English version of the journal

New Classes of Contractions in Banach Algebras with Applications

M. R. Haddadia, V. Parvanehb, M. Mursaleencd, V. Rakočeviće

a Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, 69737-69199 Iran
b Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, 67871-54699 Iran
c Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, 40402 Taiwan
d Department of Mathematics, Aligarh Muslim University, Aligarh, 202002 India
e Department of Mathematics, Faculty of Sciences and Mathematics, University of Niš, Niš, 18000 Serbia
Citations (1)
Abstract: In this paper, we introduce a new class of algebras satisfying certain conditions which has been named power algebras and we prove some fixed point theorems for a new class of contractions. We give new conditions for the existence and uniqueness of fixed points for this new class of mappings which are not a contraction in the usual algebra. Also, we introduce a new iterative algorithm for fixed-point problems in a Banach algebra. This results improve and extend the corresponding conclusions of the Ishikawa algorithm under weaker conditions and lead to stronger results. In conclusion, we give an application to nonlinear integral equations.
Keywords: Banach algebra, contraction map, fixed point, Ishikawa algorithm, integral equation.
Received: 31.12.2020
Revised: 10.04.2021
English version:
Mathematical Notes, 2021, Volume 110, Issue 4, Pages 522–531
DOI: https://doi.org/10.1134/S0001434621090224
Bibliographic databases:
Document Type: Article
Language: English
Citation: M. R. Haddadi, V. Parvaneh, M. Mursaleen, V. Rakočević, “New Classes of Contractions in Banach Algebras with Applications”, Math. Notes, 110:4 (2021), 522–531
Citation in format AMSBIB
\Bibitem{HadParMur21}
\by M.~R.~Haddadi, V.~Parvaneh, M.~Mursaleen, V.~Rako{\v{c}}evi\'c
\paper New Classes of Contractions in Banach Algebras
with Applications
\jour Math. Notes
\yr 2021
\vol 110
\issue 4
\pages 522--531
\mathnet{http://mi.mathnet.ru/mzm13304}
\crossref{https://doi.org/10.1134/S0001434621090224}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000711049900022}
\elib{https://elibrary.ru/item.asp?id=47728283}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85118175543}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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