Geodesic
On bounded metric spaces: common fixed point results with an application to nonlinear integral equations
Problemy analiza, Tome 13 (2024) no. 1, pp. 82-99.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this article, we establish some common fixed point theorems in the setting of bounded metric spaces without using neither the compactness nor the uniform convexity of the space. Some examples are built to show the superiority of the obtained results compared to the existing ones in the literature. Moreover, we apply the main result to show the existence and uniqueness of a solution for a nonlinear integral system.
Keywords: common fixed point, compactness, uniform convexity, $E$-weakly of type $T$, nonlinear integral system. 
@article{PA_2024_13_1_a5,
     author = {Y. Touail},
     title = {On bounded metric spaces: common fixed point results with an application to nonlinear integral equations},
     journal = {Problemy analiza},
     pages = {82--99},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2024_13_1_a5/}
}
TY  - JOUR
AU  - Y. Touail
TI  - On bounded metric spaces: common fixed point results with an application to nonlinear integral equations
JO  - Problemy analiza
PY  - 2024
SP  - 82
EP  - 99
VL  - 13
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2024_13_1_a5/
LA  - en
ID  - PA_2024_13_1_a5
ER  - 
%0 Journal Article
%A Y. Touail
%T On bounded metric spaces: common fixed point results with an application to nonlinear integral equations
%J Problemy analiza
%D 2024
%P 82-99
%V 13
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2024_13_1_a5/
%G en
%F PA_2024_13_1_a5
Y. Touail. On bounded metric spaces: common fixed point results with an application to nonlinear integral equations. Problemy analiza, Tome 13 (2024) no. 1, pp. 82-99. http://geodesic.mathdoc.fr/item/PA_2024_13_1_a5/

[1] Aamri M. and El Moutawakil D., “$\tau$-distance in general topological spaces with application to fixed point theory”, Southwest J. Pur. Appl. Math., 2 (2003), 1–5 | MR

[2] Alber Ya. I., Guerre-Delabriere S., “Principle of weakly contractive maps in Hilbert spaces”, Oper. Theory: Adv. Appl., 98, eds. I. Gohberg and Yu. Lyubich, Birkhauser verlag, Basel, 1997, 7–22 | DOI | MR | Zbl

[3] Browder F. E., “Nonexpansive nonlinear operators in a Banach space”, Proc. Nat. Acad. Sei. U.S.A, 54 (1965) | MR

[4] Edelstein M., “On fixed and periodic points under contractive mappings”, J. London Math. Soc., 37 (1962), 74–79 | DOI | MR | Zbl

[5] Göhde D., “Zum prinzip der kontraktiven Abbildung”, Math. Nachr., 30 (1965), 251–258 | DOI | MR | Zbl

[6] Jungck G., Rhoades B. E., “Fixed point for set valued functions without continuity”, Indian J. Pure Appl. Math., 29:3 (1998), 227–238 | MR | Zbl

[7] Karapinar E., Yüksel U., “Some Common Fixed Point Theorems in Partial Metric Spaces”, J. Appl. Math., 2011, 263621, 16 pp. | DOI | MR | Zbl

[8] Karapinar E., Kumam P., Salimi P., “On a $\alpha$-$\psi$-Meir-Keeler contractive mappings”, Fixed Point Theory Appl., 2013, 94 | DOI | MR | Zbl

[9] Khalehoghli S., Rahimi H., Eshaghi M., “Fixed point theorems in R-metric spaces with applications”, AIMS Math., 5:4 (2020), 3125–3137 | DOI | MR | Zbl

[10] Künzi H.-P. A., Pajoohesh H., Schellekens M. P., “Partial quasi-metrics”, Theor. Comp. Sc., 365:3 (2006), 237–246 | DOI | MR | Zbl

[11] Matthews S. G., “Partial metric topology”, Proc. 8th Summ. Confer. Gener. Topo. Appl., Annals of the New York Academy of Sciences, 728, 1994, 183–197 | DOI | MR | Zbl

[12] Nemytzki V. V., “The fixed point method in analysis”, Usp. Mat. Nauk, 1 (1936), 141–174 (in Russian)

[13] O'Neill S. J., Two topologies are better than one, Tech. Rep., University of Warwick, Coventry, UK, 1995 | Zbl

[14] Radenović S., Kadelburg Z., Jandrlić D., Jandrlić A., “Some results on weak contraction maps”, Bull. Iranian Math. Soc., 38 (2012), 625–645 | MR | Zbl

[15] Rhoades B. E., “Some theorems on weakly contractive maps”, Nonl. Anal., 47 (2001), 2683–2693 | DOI | MR | Zbl

[16] Rosa V. L., Vetro P., “Common fixed points for a $\alpha$-$\psi$-$\phi$-contractions in generalized metric spaces”, Nonl. Anal.: Model. and Cont., 19:1 (2014), 43–54 | DOI | MR | Zbl

[17] Schellekens M. P., “A characterization of partial metrizability: domains are quantifiable”, Theoret. Comput. Sc., 305:13 (2013), 409–432 | DOI | MR

[18] Touail Y., El Moutawakil D., Bennani S., “Fixed Point theorems for contractive selfmappings of a bounded metric space”, J. Func. Spac. Volume, 2019, 4175807, 3 pp. | DOI | MR | Zbl

[19] Touail Y., El Moutawakil D., “Fixed point results for new type of multivalued mappings in bounded metric spaces with an application”, Ricerche Mat., 71 (2022), 315–323 | DOI | MR | Zbl

[20] 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., 2021, 903–911 | DOI | MR

[21] Touail Y., El Moutawakil D., “Fixed point theorems for new contractions with application in dynamic programming”, Vestnik St.Petersb. Univ. Math., 54 (2021), 206–212 | DOI | MR | Zbl

[22] Touail Y., El Moutawakil D., “Some new common fixed point theorems for contractive selfmappings with applications”, Asian. Eur. J. Math., 15:4 (2022), 2250080 | DOI | MR | Zbl

[23] Touail Y., El Moutawakil D., “Fixed point theorems on orthogonal complete metric spaces with an application”, Int. J. Nonl. Anal. Appl., 2021, 1801–1809 | DOI | MR

[24] Touail Y., El Moutawakil D., “$\perp_{\psi F} $-contractions and some fixed point results on generalized orthogonal sets”, Rend. Circ. Mat. Palermo, II. Ser., 2020 | DOI | MR

[25] Touail Y., Jaid A., El Moutawakil D., “New contribution in fixed point theory via an auxiliary function with an application”, Ricerche Mat., 72 (2023), 181–191 | DOI | MR

[26] Touail Y., “On multivalued $\perp_{ \psi F} $-contractions on generalized orthogonal sets with an application to integral inclusions”, Probl. Anal. Issues Anal., 29:3 (2022), 109–124 | DOI | MR | Zbl

[27] Touail Y., “A New Generalization of Metric Spaces Satisfying the $T_2$-Separation Axiom and Some Related Fixed Point Results”, Russ. Math., 67 (2023), 76–86 | DOI | MR | Zbl