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System of generalized nonlinear variational-like inequalities and nearly asymptotically nonexpansive mappings: graph convergence and fixed point problems

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Abstract

In this paper, with the goal of investigating the problem of finding a common element of the set of fixed points of a nearly asymptotically nonexpansive mapping and the set of solutions of a system of generalized nonlinear variational-like inequalities, an iterative algorithm is proposed. The notions of graph convergence and P–\(\eta\)-proximal point mapping are used and a new equivalence relationship between graph convergence and proximal-point mappings convergence of a sequence of lower semicontinuous and \(\eta\)-subdifferentiable proper functionals is established. Finally, the strong convergence of the sequence generated by our suggested iterative algorithm to a common element of the two sets mentioned above are demonstrated.

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Acknowledgements

The authors express their sincere thanks to the referee and editor for their advice to improve the quality of this paper.

Author information

Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran

    Javad Balooee

  2. The Key Laboratory of Intelligent Information and Big Data Processing of NingXia Province, and Health Big Data Research Institute, North Minzu University, 750021, Yinchuan, China

    Mihai Postolache

  3. Department of Mathematics and Informatics, University ”Politehnica” of Bucharest, 060042, Bucharest, Romania

    Mihai Postolache

  4. Gh. Mihoc-C. Iacob Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Bucharest, 050711, Romania

    Mihai Postolache

  5. School of Mathematical Sciences, Tiangong University, 300387, Tianjin, China

    Yonghong Yao

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  1. Javad Balooee
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  2. Mihai Postolache
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  3. Yonghong Yao
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Correspondence to Mihai Postolache.

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Communicated by  Gradimir V. Milovanović.

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Balooee, J., Postolache, M. & Yao, Y. System of generalized nonlinear variational-like inequalities and nearly asymptotically nonexpansive mappings: graph convergence and fixed point problems. Ann. Funct. Anal. 13, 68 (2022). https://doi.org/10.1007/s43034-022-00212-6

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  • DOI: https://doi.org/10.1007/s43034-022-00212-6

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