Convergence of a Four-Step Iteration Process for G-nonexpansive Mappings in Banach Spaces with a Digraph

Year 2023, Volume: 4 Issue: 2, 96 - 106, 31.07.2023

Esra Yolacan

Abstract

This review reckons with iterative scheme of Thianwan to approximate a common fixed point for four G-nonexpansive mappings (tersely G-nm). We verify several convergence results for in this way mappings in Banach space by dint of a digraph.

Keywords

fixed point, digraph, G-Nonexpansive mappings

Supporting Institution

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Project Number

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Thanks

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References

• Kettapun A., Kananthai A., Suantai S., A new approximation method for common fixed points of a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces, Computers and Mathematics with Applications, 60, 1430-1439, 2010.
• Jachymski J., The contraction principle for mappings on a metric space with a graph, Proceeding of the American Mathematical Society, 136, 1359-1373, 2008.
• Alfuraidan M.R., Khamsi M.A., Fixed points of monotone nonexpansive mappings on a hyperbolic metric space with a graph, Fixed Point Theory and Applications, 2015:44, 2015.
• Tripak O., Common fixed points of Gnonexpansive mappings on Banach spaces with a graph, Fixed Point Theory and Applications, 2016:87, 2016.
• Suparatulatorn R., Cholamjiak W., Suantai S., A modified Siteration process for Gnonexpansive mappings in Banach spaces with a graph, Numerical Algorithms, 77, 479-490, 2018.
• Hunde T.W., Sangago M.G., Zegeye H., Approximation of a common fixed point of a family of Gnonexpansive mappings in Banach spaces with a graph, International Journal of Advances in Mathematics, 6, 137-152, 2017.
• Sridarat P., Suparatulatorn R., Suantai S., Cho Y.J., Convergence analysis of SPiteration for Gnonexpansive mappings with directed graphs, Bulletin of the Malaysian Mathematical Sciences Society, 19, 1-20, 2018.
• Alfuraidan M.R., Fixed points of monotone nonexpansive mappings with a graph, Fixed Point Theory and Applications, 2015:49, 2015.
• Shahzad N., Al-Dubiban P., Approximating common fixed points of nonexpansive mappings in Banach spaces, Georgian Mathematical Journal, 13(3), 529-537, 2006.
• Sahu J., Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bulletin of the Australian Mathematical Society, 43, 153-159, 1991.
• Tan K.K., Xu H.K., Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, Journal of Mathematical Analysis and Applications, 178, 301-308, 1993.
• Thianwan S., Weak and strong convergence theorems for new iterations with errors for nonexpansive nonself-mapping, Thai Journal of Mathematics, Special Issue (Annual Meeting in Mathematics), 27- 38, 2008.
• Kızıltunç H., Özdemir M., Akbulut S., Common fixed points for two nonexpansive nonself-mappings with errors in Banach spaces, The Arabian Journal for Science and Engineering, Vol.35, Number 2D, 215-224, 2010.
• Shahzad N., Approximating fixed points of non-self nonexpansive mappings in Banach spaces, Nonlinear Analysis, 61(6), 1031-1039, 2005.
• Phuengrattana W., Suantai S., On the rate of convergence of Mann, Ishikawa, Noor and SP iterations for continuous functions on an arbitrary interval, Journal of Computational and Applied Mathematics, 235, 3006-3014, 2011.
• Şahin A., Başarır M., On the strong and Δconvergence of SPiteration on CATˆ0  space, Journal of Inequalities and Applications, 2013:311, 2013.