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. |
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| 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] |
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| Database: | Engineering Source |
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| 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] |
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| ISSN: | 10853375 |
| DOI: | 10.1155/aaa/6651340 |
