Abstract
In this paper, we employ the notion asymptotic contraction of Kirk (J Math Anal Appl 277:645–650, 2003) to obtain some common fixed point results of a pair of mappings and a finite family of mappings. To execute this, we introduce the notion of asymptotic contractions in pair for a finite family of mappings. Then, we obtain our prescribed common fixed point results using these asymptotic contractions in pair concepts. After this, we apply these results to analyze the unique common solution to a certain kind of pair of matrix equations. Finally, we provide some numerical examples to authenticate our results using figurative presentations.
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Acknowledgements
The authors are grateful to the anonymous referees for their valuable comments and suggestions. The research is funded by the Ministry of Human Resource and Development, Government of India.
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Communicated by Jinyun Yuan.
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Bera, A., Dey, L.K., Garai, H. et al. Common fixed points via asymptotic contraction and application to matrix equations. Comp. Appl. Math. 39, 301 (2020). https://doi.org/10.1007/s40314-020-01358-6
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DOI: https://doi.org/10.1007/s40314-020-01358-6