Fixed point results using $\alpha$-admissibility
DOI :
https://doi.org/10.5269/bspm.75772Résumé
In this article, using the notion of $\alpha$-admissibility, we present a new class of condensing mappings. Via this class, we prove some extensions of Darbo fixed point theorem. Moreover, we give an example to illustrate the usability of the achieved results.
Références
1. Banach, S., Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund.Math., 3(1), 133-181 (1922).
2. Banas, J. and Goebel, K., Measures of Non-compactness in Banach Spaces, Marcel Dekker, New York (1980).
3. Brouwer, L. E. J., Uber abbildung von mannigfaltigkeiten, Math. Ann., 71(1), 97-115 (1911).
4. Darbo, G., Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova., 24, 84-92 (1955). Results 5
5. Imdad, M., Khan, A. R., Saleh, H. N., Alfaqih, W. M., Some φ-fixed point results for (F,φ,α-ψ)-contractive type mappings with applications. Mathematics, 7(2), 122 (2019). https://doi.org/10.3390/math7020122
6. Kuratowski, C., Sur les espaces complets, Fund. Math., 1(15), 301-309 (1930).
7. Raji, M., Generalized α-ψ-contractive type mappings and related coincidence fixed point theorems with applications. The Journal of Analysis, 31(2), 1241-1256 (2023). https://doi.org/10.1007/s41478-022-00498-8
8. Samet, B., Vetro, C., Vetro, P., Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal., 75(4), 2154-2165 (2012). https://doi.org/10.1016/j.na.2011.10.014
9. Samet, B., Fixed points for α-ψ-contractive mappings with an application to quadratic integral equations. Electron. J. Differ. Equ, 152 (2014).
10. Schauder, J., Der Fixpunktsatz in Funktional-raumen, Studia Math., 2(1), 171-180 (1930).
11. Touail, Y., Jaid, A., El Moutawakil, D., Fixed Point Theorem via Measure of Non-Compactness for a New Kind of Contractions. Vestnik St. Petersburg University, Mathematics, 56(2), 198-202 (2023). https://doi.org/10.1134/S1063454123020164
12. Touail, Y., Jaid, A., El Moutawakil, D., A note on common fixed point theorems in a bounded metric space. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 27(2), 241-249 (2023). https://doi.org/10.14498/vsgtu1940
13. Touail, Y., Set-valued mappings: fixed point results with β-function and some applications. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 63, 61-79 (2024). https://doi.org/10.35634/2226-3594-2024-63-05
2. Banas, J. and Goebel, K., Measures of Non-compactness in Banach Spaces, Marcel Dekker, New York (1980).
3. Brouwer, L. E. J., Uber abbildung von mannigfaltigkeiten, Math. Ann., 71(1), 97-115 (1911).
4. Darbo, G., Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova., 24, 84-92 (1955). Results 5
5. Imdad, M., Khan, A. R., Saleh, H. N., Alfaqih, W. M., Some φ-fixed point results for (F,φ,α-ψ)-contractive type mappings with applications. Mathematics, 7(2), 122 (2019). https://doi.org/10.3390/math7020122
6. Kuratowski, C., Sur les espaces complets, Fund. Math., 1(15), 301-309 (1930).
7. Raji, M., Generalized α-ψ-contractive type mappings and related coincidence fixed point theorems with applications. The Journal of Analysis, 31(2), 1241-1256 (2023). https://doi.org/10.1007/s41478-022-00498-8
8. Samet, B., Vetro, C., Vetro, P., Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal., 75(4), 2154-2165 (2012). https://doi.org/10.1016/j.na.2011.10.014
9. Samet, B., Fixed points for α-ψ-contractive mappings with an application to quadratic integral equations. Electron. J. Differ. Equ, 152 (2014).
10. Schauder, J., Der Fixpunktsatz in Funktional-raumen, Studia Math., 2(1), 171-180 (1930).
11. Touail, Y., Jaid, A., El Moutawakil, D., Fixed Point Theorem via Measure of Non-Compactness for a New Kind of Contractions. Vestnik St. Petersburg University, Mathematics, 56(2), 198-202 (2023). https://doi.org/10.1134/S1063454123020164
12. Touail, Y., Jaid, A., El Moutawakil, D., A note on common fixed point theorems in a bounded metric space. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 27(2), 241-249 (2023). https://doi.org/10.14498/vsgtu1940
13. Touail, Y., Set-valued mappings: fixed point results with β-function and some applications. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 63, 61-79 (2024). https://doi.org/10.35634/2226-3594-2024-63-05
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Publié
2025-08-10
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Research Articles
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When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
Comment citer
Jaid, A., Touail, Y., & Moutawakil, D. E. . (2025). Fixed point results using $\alpha$-admissibility. Boletim Da Sociedade Paranaense De Matemática, 43, 1-5. https://doi.org/10.5269/bspm.75772
