Fixed point theorem via measure of non-compactness for a new kind of contractions
DOI:
https://doi.org/10.21638/spbu01.2023.208Abstract
In this paper, we will use the notion of α-admissible mappings in Banach spaces, to introduce the concept of Tβ-contractive mappings and establish a fixed point theorem for this type of contractions. Our theorems generalize and improve many results in the literature. Moreover, we apply the main result to prove the existence of a solution for Volterra-integral equation, under more general assumptions than previously made.Keywords:
fixed point, measure of non-compactness, α-admissible, Tβ-contractive mapping, regularity
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References
Литература
1. Kuratowski K. Sur les espaces complets. Fundam. Math. 15 (1930), 301-309.
2. Banach S. Sur les op´erations dans les ensembles abstraits et leur applications aux ´equations int´egrales. Fund. Math. 3, 133-181 (1922).
3. Schauder J. Der fixpunktsatz in funktionalr¨aumen. Studia Math. 2, 171-180 (1930).
4. Sadovskii B. N. A fixed point principle. Functional Analysis and Its Applications 1, 74-76 (1967).
5. Samet B., Vetro C., Vetro P. Fixed point theorems for α−ψ-contractive type mappings. Nonlinear Analysis 75 (4), 2154-2165 (2012). https://doi.org/10.1016/j.na.2011.10.014
6. Aghajani A., Pourhad E. Application of measure of noncompactness to l1-solvability of finite systems of second order differential equations. Bull. Belg. Math. Soc. Simon Stevin 22 (1), 105-118 (2015). https://doi.org/10.36045/bbms/1426856862
7. Touail Y., El Moutawakil D., Bennani S. Fixed point theorems for contractive selfmappings of a bounded metric space. Journal of Function Spaces 2019, Article ID 4175807 (2019).
8. Touail Y., El Moutawakil D. Fixed point results for new type of multivalued mappings in bounded metric spaces with an application. Ricerche di Matematica 71, 315-323 (2022). https://doi.org/10.1007/s11587-020-00498-5
9. Touail Y., El Moutawakil D. New common fixed point theorems for contractive self mappings and an application to nonlinear differential equations. Int. J. Nonlinear Anal. Appl. 12 (1), 903-911 (2021). https://doi.org/10.22075/ijnaa.2021.21318.2245
10. Touail Y., El Moutawakil D. Fixed point theorems for new contractions with application in dynamic programming. Vestnik St Petersburg University. Mathematics 54, iss. 1, 206-212 (2021). https://doi.org/10.1134/S1063454121020126
11. Touail Y., El Moutawakil D. Some new common fixed point theorems for contractive self mappings with applications. Asian-European Journal of Mathematics 2250080 (2021). https://dx.doi.org/10.1142/s1793557122500802
12. Touail Y., El Moutawakil D. Fixed point theorems on orthogonal complete metric spaces with an application. International Journal of Nonlinear Analysis and Applications 12 (2), 1801-1809. https://doi.org/10.22075/ijnaa.2021.23033.2464 (2021).
13. Touail Y., Jaid A., El Moutawakil D. New contribution in fixed point theory via an auxiliary function with an application. Ricerche di Matematica (2021). https://doi.org/10.1007/s11587-021-00645-6
14. Touail Y. On multivalued ⊥ψF-contractions on generalized orthogonal sets with an aplication to integral inclusions, probl. Anal. Issues Anal. 11 (29), no. 3, 109-124 (2022). https://doi.org/10.15393/j3.art.2022.12030
15. Touail Y., Jaid A., El Moutawakil D. Fixed point results for condensing operators via measure of non-compactness. Vestnik St Petersburg University. Mathematics 55, 347-352 (2022). https://doi.org/10.1134/S1063454122030153
16. Banas J., Goebel K. Measures of non-compactness in Banach Spaces. New York, Marcel Dekker (1980).
17. Darbo G. Punti uniti in trasformazioni a codominio non compatto. Rendiconti del Seminario Matematico della Universit`a di Padova 24, 84-92 (1955).
References
1. Kuratowski K. Sur les espaces complets. Fundam. Math. 15 (1930), 301-309.
2. Banach S. Sur les op´erations dans les ensembles abstraits et leur applications aux ´equations int´egrales. Fund. Math. 3, 133-181 (1922).
3. Schauder J. Der fixpunktsatz in funktionalr¨aumen. Studia Math. 2, 171-180 (1930).
4. Sadovskii B. N. A fixed point principle. Functional Analysis and Its Applications 1, 74-76 (1967).
5. Samet B., Vetro C., Vetro P. Fixed point theorems for α−ψ-contractive type mappings. Nonlinear Analysis 75 (4), 2154-2165 (2012). https://doi.org/10.1016/j.na.2011.10.014
6. Aghajani A., Pourhad E. Application of measure of noncompactness to l1-solvability of finite systems of second order differential equations. Bull. Belg. Math. Soc. Simon Stevin 22 (1), 105-118 (2015). https://doi.org/10.36045/bbms/1426856862
7. Touail Y., El Moutawakil D., Bennani S. Fixed point theorems for contractive selfmappings of a bounded metric space. Journal of Function Spaces 2019, Article ID 4175807 (2019).
8. Touail Y., El Moutawakil D. Fixed point results for new type of multivalued mappings in bounded metric spaces with an application. Ricerche di Matematica 71, 315-323 (2022). https://doi.org/10.1007/s11587-020-00498-5
9. Touail Y., El Moutawakil D. New common fixed point theorems for contractive self mappings and an application to nonlinear differential equations. Int. J. Nonlinear Anal. Appl. 12 (1), 903-911 (2021). https://doi.org/10.22075/ijnaa.2021.21318.2245
10. Touail Y., El Moutawakil D. Fixed point theorems for new contractions with application in dynamic programming. Vestnik St Petersburg University. Mathematics 54, iss. 1, 206-212 (2021). https://doi.org/10.1134/S1063454121020126
11. Touail Y., El Moutawakil D. Some new common fixed point theorems for contractive self mappings with applications. Asian-European Journal of Mathematics 2250080 (2021). https://dx.doi.org/10.1142/s1793557122500802
12. Touail Y., El Moutawakil D. Fixed point theorems on orthogonal complete metric spaces with an application. International Journal of Nonlinear Analysis and Applications 12 (2), 1801-1809. https://doi.org/10.22075/ijnaa.2021.23033.2464 (2021).
13. Touail Y., Jaid A., El Moutawakil D. New contribution in fixed point theory via an auxiliary function with an application. Ricerche di Matematica (2021). https://doi.org/10.1007/s11587-021-00645-6
14. Touail Y. On multivalued ⊥ψF-contractions on generalized orthogonal sets with an aplication to integral inclusions, probl. Anal. Issues Anal. 11 (29), no. 3, 109-124 (2022). https://doi.org/10.15393/j3.art.2022.12030
15. Touail Y., Jaid A., El Moutawakil D. Fixed point results for condensing operators via measure of non-compactness. Vestnik St Petersburg University. Mathematics 55, 347-352 (2022). https://doi.org/10.1134/S1063454122030153
16. Banas J., Goebel K. Measures of non-compactness in Banach Spaces. New York, Marcel Dekker (1980).
17. Darbo G. Punti uniti in trasformazioni a codominio non compatto. Rendiconti del Seminario Matematico della Universit`a di Padova 24, 84-92 (1955).
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Published
2023-05-10
How to Cite
Touail, Y., Jaid, A., & El Moutawakil, D. (2023). Fixed point theorem via measure of non-compactness for a new kind of contractions. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10(2), 270–276. https://doi.org/10.21638/spbu01.2023.208
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Mathematics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
