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Existence of Nonstationary Fixed Point Results on Multivalued Maps and Fractal Construction Using Trajectories.

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Title: Existence of Nonstationary Fixed Point Results on Multivalued Maps and Fractal Construction Using Trajectories.
Authors: Jothy, A. Herminau1 (AUTHOR), Theivaraman, R.2 (AUTHOR), Shukla, Rahul3 (AUTHOR) rshukla@wsu.ac.za, Srinivasan, P. S.1 (AUTHOR), Deepali (AUTHOR) dedeepali@wiley.com
Source: Abstract & Applied Analysis. 4/24/2026, Vol. 2026, p1-6. 6p.
Subjects: Fixed point theory, Set-valued maps, Mathematical sequences, Fractals, Hausdorff measures, Metric spaces, Mathematics theorems
Abstract: In this paper, we study the forward and backward trajectories associated with multivalued mappings in a complete metric space. We analyze the convergence of sequences generated by multivalued function systems (SMFSs) toward an attractor under the Hausdorff metric. A generalized class of multivalued contractions defined via a comparison function is introduced, extending several existing contraction principles. Under appropriate assumptions, we establish sufficient conditions ensuring the convergence of trajectories to an attractor. Our results unify and generalize various known fixed point and convergence theorems in the setting of multivalued dynamics. MSC2020 Classification: 28A80, 47H10, 54E50 54H25 [ABSTRACT FROM AUTHOR]
Copyright of Abstract & Applied Analysis is the property of Wiley-Blackwell 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.)
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  Data: Existence of Nonstationary Fixed Point Results on Multivalued Maps and Fractal Construction Using Trajectories.
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  Data: <searchLink fieldCode="DE" term="%22Fixed+point+theory%22">Fixed point theory</searchLink><br /><searchLink fieldCode="DE" term="%22Set-valued+maps%22">Set-valued maps</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+sequences%22">Mathematical sequences</searchLink><br /><searchLink fieldCode="DE" term="%22Fractals%22">Fractals</searchLink><br /><searchLink fieldCode="DE" term="%22Hausdorff+measures%22">Hausdorff measures</searchLink><br /><searchLink fieldCode="DE" term="%22Metric+spaces%22">Metric spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+theorems%22">Mathematics theorems</searchLink>
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  Data: In this paper, we study the forward and backward trajectories associated with multivalued mappings in a complete metric space. We analyze the convergence of sequences generated by multivalued function systems (SMFSs) toward an attractor under the Hausdorff metric. A generalized class of multivalued contractions defined via a comparison function is introduced, extending several existing contraction principles. Under appropriate assumptions, we establish sufficient conditions ensuring the convergence of trajectories to an attractor. Our results unify and generalize various known fixed point and convergence theorems in the setting of multivalued dynamics. MSC2020 Classification: 28A80, 47H10, 54E50 54H25 [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Abstract & Applied Analysis is the property of Wiley-Blackwell 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: 10.1155/aaa/6651340
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      – Code: eng
        Text: English
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      – SubjectFull: Set-valued maps
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      – SubjectFull: Mathematical sequences
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      – SubjectFull: Fractals
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      – SubjectFull: Hausdorff measures
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      – SubjectFull: Metric spaces
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      – SubjectFull: Mathematics theorems
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      – TitleFull: Existence of Nonstationary Fixed Point Results on Multivalued Maps and Fractal Construction Using Trajectories.
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              Text: 4/24/2026
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              Y: 2026
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