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Ergodic theorems for hybrid sequences in a Hilbert space with applications.

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Title: Ergodic theorems for hybrid sequences in a Hilbert space with applications.
Authors: Djafari Rouhani, Behzad1 behzad@math.utep.edu
Source: Journal of Mathematical Analysis & Applications. Jan2014, Vol. 409 Issue 1, p205-211. 7p.
Subjects: Mathematics theorems, Hilbert space, Generalization, Mathematical sequences, Fixed point theory, Stochastic convergence
Abstract: Abstract: In this paper, we introduce the notion of generalized hybrid sequences, extending the notion of nonexpansive sequences introduced and studied in our previous work Djafari Rouhani (1981, 1990, 1990, 1997, 2002, 2004, 2002) [2–8], and prove ergodic and convergence theorems for such sequences in a Hilbert space . Subsequently, we apply our results to prove new fixed point theorems for generalized hybrid mappings, first introduced in Kocourek et al. (2010) [14], Takahashi and Takeuchi (2011) [20], defined on arbitrary nonempty subsets of . [Copyright &y& Elsevier]
Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 90067252
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Ergodic theorems for hybrid sequences in a Hilbert space with applications.
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  Data: <searchLink fieldCode="AR" term="%22Djafari+Rouhani%2C+Behzad%22">Djafari Rouhani, Behzad</searchLink><relatesTo>1</relatesTo><i> behzad@math.utep.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Mathematical+Analysis+%26+Applications%22">Journal of Mathematical Analysis & Applications</searchLink>. Jan2014, Vol. 409 Issue 1, p205-211. 7p.
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  Data: <searchLink fieldCode="DE" term="%22Mathematics+theorems%22">Mathematics theorems</searchLink><br /><searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br /><searchLink fieldCode="DE" term="%22Generalization%22">Generalization</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+sequences%22">Mathematical sequences</searchLink><br /><searchLink fieldCode="DE" term="%22Fixed+point+theory%22">Fixed point theory</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+convergence%22">Stochastic convergence</searchLink>
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  Label: Abstract
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  Data: Abstract: In this paper, we introduce the notion of generalized hybrid sequences, extending the notion of nonexpansive sequences introduced and studied in our previous work Djafari Rouhani (1981, 1990, 1990, 1997, 2002, 2004, 2002) [2–8], and prove ergodic and convergence theorems for such sequences in a Hilbert space . Subsequently, we apply our results to prove new fixed point theorems for generalized hybrid mappings, first introduced in Kocourek et al. (2010) [14], Takahashi and Takeuchi (2011) [20], defined on arbitrary nonempty subsets of . [Copyright &y& Elsevier]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jmaa.2013.06.067
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      – Code: eng
        Text: English
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        PageCount: 7
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      – SubjectFull: Mathematics theorems
        Type: general
      – SubjectFull: Hilbert space
        Type: general
      – SubjectFull: Generalization
        Type: general
      – SubjectFull: Mathematical sequences
        Type: general
      – SubjectFull: Fixed point theory
        Type: general
      – SubjectFull: Stochastic convergence
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      – TitleFull: Ergodic theorems for hybrid sequences in a Hilbert space with applications.
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              Text: Jan2014
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