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Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero


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CiteScore 2018: 0.47
SCImago Journal Rank (SJR) 2018: 0.265
Source Normalized Impact per Paper (SNIP) 2018: 0.714

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2391-4661
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Volume 51, Issue 1

Issues

Ergodic and fixed point theorems for sequences and nonlinear mappings in a Hilbert space

Behzad Djafari Rouhani
  • Department of Mathematical Sciences, University of Texas at El Paso, 500 W. University Avenue, El Paso, Texas 79968 USA
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Published Online: 2018-04-13 | DOI: https://doi.org/10.1515/dema-2018-0005

Abstract

In this paper, we introduce the notion of 2-generalized hybrid sequences, extending the notion of nonexpansive and hybrid sequences introduced and studied in our previous work [Djafari Rouhani B., Ergodic theorems for nonexpansive sequences in Hilbert spaces and related problems, Ph.D. thesis, YaleUniversity, 1981; and other published in J. Math. Anal. Appl., 1990, 2002, and 2014; Nonlinear Anal., 1997, 2002, and 2004], and prove ergodic and convergence theorems for such sequences in a Hilbert space H. Subsequently, we apply our results to prove new fixed point theorems for 2-generalized hybrid mappings, first introduced in [Maruyama T., Takahashi W., Yao M., Fixed point and mean ergodic theorems for new nonlinear mappings in Hilbert spaces, J. Nonlinear Convex Anal., 2011, 12, 185-197] and further studied in [Lin L.-J., Takahashi W., Attractive point theorems and ergodic theorems for nonlinear mappings in Hilbert spaces, Taiwanese J. Math., 2012, 16, 1763-1779], defined on arbitrary nonempty subsets of H.

Keywords: Ergodic theorem; asymptotically regular; weak convergence theorem; generalized hybrid sequence; fixed point; absolute fixed point

MSC 2010: 47H09; 47H10; 47H05

References

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About the article

Received: 2017-11-07

Accepted: 2018-03-03

Published Online: 2018-04-13


Citation Information: Demonstratio Mathematica, Volume 51, Issue 1, Pages 27–36, ISSN (Online) 2391-4661, DOI: https://doi.org/10.1515/dema-2018-0005.

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© 2018 Behzad Djafari Rouhani. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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