Fixed point results for condensing operators via measure of non-compactness
DOI:
https://doi.org/10.21638/spbu01.2022.314Abstract
In this paper, we prove some fixed point theorems for condensing operators in the setting of Banach spaces via measure of non-compactness, without using regularity. Our results improve and generalize many known results in the literature.Keywords:
fixed point, measure of non-compactness, regularity
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References
Литература
1. Schauder J. Der Fixpunktsatz in Funktionalr¨aumen. Studia Math. 2, 171-180 (1930).
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. Agarwal R.P., Arshad S., O’Regan D., Lupulescu V. A Schauder fixed point theorem in semilinear spaces and applications. Fixed Point Theory Appl. 2013, 306 (2013). https://doi.org/10.1186/1687-1812-2013-306
4. Kuratowski K. Sur les espaces complets. Fundam. Math. 15, 301-309 (1930).
5. Darbo G. Punti uniti in trasformazioni a codominio non compatto. Rend. Sem. Mat. Univ. Padova 24, 84-92 (1955).
6. Sadovskii B.N. A fixed-point principle. Funct. Anal. Its Appl. 1, 151-153 (1967). https://doi.org/10.1007/BF01076087
7. Krasnosel’skii M.A. Two remarks on the method of successive approximations. Uspekhi Matematicheskikh Nauk 10, 123-127 (1955).
8. Burton T. A fixed-point theorem of Krasnosel’skii. Appl. Math. Lett. 11, 85-88 (1998).
9. Dhage B.C. Remarks on two fixed-point theorems involving the sum and the product of two operators. Computers and Mathematics with Applications 46, 1779-1785 (2003).
10. Edelstein M. On fixed and periodic points under contractive mappings. J. of Lon. Math. Soc. 37 (1), 74-79 (1962).
11. Touail Y., El Moutawakil D., Bennani S. Fixed Point theorems for contractive selfmappings of a bounded metric space. J. Func. Spac. 2019, 4175807 (2019). https://doi.org/10.1155/2019/4175807
12. Touail Y., El Moutawakil D. Fixed point results for new type of multivalued mappings in bounded metric spaces with an application. Ricerche di Matematica (2020). https://doi.org/10.1007/s11587-020-00498-5
13. 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
14. Touail Y., El Moutawakil D. Fixed Point Theorems for New Contractions with Application in Dynamic Programming. Vestnik St Petersb. Univ. Math. 54, 206-212 (2021). https://doi.org/10.1134/S1063454121020126
15. Touail Y., El Moutawakil D. Some new common fixed point theorems for contractive selfmappings with applications. Asian. Eur. J. Math. 15 (4), 2250080 (2022). https://doi.org/10.1142/S1793557122500802
16. Touail Y., El Moutawakil D. Fixed point theorems on orthogonal complete metric spaces with an application. Int. J. Nonlinear Anal. Appl. 12 (2), 1801-1809 (2021). https://doi.org/10.22075/IJNAA.2021.23033.2464
17. 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
18. Banas J., Goebel K. Measures of Non-compactness in Banach Spaces. New York, Marcel Dekker (1980).
References
1. Schauder J. Der Fixpunktsatz in Funktionalr¨aumen. Studia Math. 2, 171-180 (1930).
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. Agarwal R.P., Arshad S., O’Regan D., Lupulescu V. A Schauder fixed point theorem in semilinear spaces and applications. Fixed Point Theory Appl. 2013, 306 (2013). https://doi.org/10.1186/1687-1812-2013-306
4. Kuratowski K. Sur les espaces complets. Fundam. Math. 15, 301-309 (1930).
5. Darbo G. Punti uniti in trasformazioni a codominio non compatto. Rend. Sem. Mat. Univ. Padova 24, 84-92 (1955).
6. Sadovskii B.N. A fixed-point principle. Funct. Anal. Its Appl. 1, 151-153 (1967). https://doi.org/10.1007/BF01076087
7. Krasnosel’skii M.A. Two remarks on the method of successive approximations. Uspekhi Matematicheskikh Nauk 10, 123-127 (1955).
8. Burton T. A fixed-point theorem of Krasnosel’skii. Appl. Math. Lett. 11, 85-88 (1998).
9. Dhage B.C. Remarks on two fixed-point theorems involving the sum and the product of two operators. Computers and Mathematics with Applications 46, 1779-1785 (2003).
10. Edelstein M. On fixed and periodic points under contractive mappings. J. of Lon. Math. Soc. 37 (1), 74-79 (1962).
11. Touail Y., El Moutawakil D., Bennani S. Fixed Point theorems for contractive selfmappings of a bounded metric space. J. Func. Spac. 2019, 4175807 (2019). https://doi.org/10.1155/2019/4175807
12. Touail Y., El Moutawakil D. Fixed point results for new type of multivalued mappings in bounded metric spaces with an application. Ricerche di Matematica (2020). https://doi.org/10.1007/s11587-020-00498-5
13. 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
14. Touail Y., El Moutawakil D. Fixed Point Theorems for New Contractions with Application in Dynamic Programming. Vestnik St Petersb. Univ. Math. 54, 206-212 (2021). https://doi.org/10.1134/S1063454121020126
15. Touail Y., El Moutawakil D. Some new common fixed point theorems for contractive selfmappings with applications. Asian. Eur. J. Math. 15 (4), 2250080 (2022). https://doi.org/10.1142/S1793557122500802
16. Touail Y., El Moutawakil D. Fixed point theorems on orthogonal complete metric spaces with an application. Int. J. Nonlinear Anal. Appl. 12 (2), 1801-1809 (2021). https://doi.org/10.22075/IJNAA.2021.23033.2464
17. 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
18. Banas J., Goebel K. Measures of Non-compactness in Banach Spaces. New York, Marcel Dekker (1980).
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Published
2022-10-10
How to Cite
Touail, Y., Jaid, A., & El Moutawakil, D. (2022). Fixed point results for condensing operators via measure of non-compactness. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9(3), 542–549. https://doi.org/10.21638/spbu01.2022.314
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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.
