Well-posedness of the fixed point problem for certain asymptotically regular mappings

Mohamed Akkouchi

Published: 2009-09-30

Vol. 23 (2009)

Well-posedness of the fixed point problem for certain asymptotically regular mappings

Mohamed Akkouchi

Abstract

We study the well-posedness of the fixed point problem for asymptotically regular self-mappings of a complete metric space (X,d) which satisfy the contractive condition (2.1) described below. This contractive condition is a variant of the contractive condition considered in [6]. The results of this paper provide some improvements and extensions to the results of Ciric [6], Sharma and Yuel [19], and Guay and Singh [7]. This work is inspired and motivated by the paper [6].

Keywords:

well-posedness , fixed point problem , fixed points , self-mappings , asymptotically regular mappings , complete and non complete metric spaces , orbitally complete spaces

Download files

PDF

Citation rules

Akkouchi, M. (2009). Well-posedness of the fixed point problem for certain asymptotically regular mappings. Annales Mathematicae Silesianae, 23, 43–52. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14041

Similar Articles

Binayak S. Choudhury, Nikhilesh Metiya, Sunirmal Kundu, Debashis Khatua, Existence, data dependence and stability of fixed points of multivalued maps in incomplete metric spaces , Annales Mathematicae Silesianae: Vol. 37 No. 1 (2023)
Valeriu Popa, Alina-Mihaela Patriciu, Fixed point theorems for two pairs of mappings satisfying a new type of common limit range property in G_p metric spaces , Annales Mathematicae Silesianae: Vol. 32 (2018)
Valeriu Popa, Alina-Mihaela Patriciu, Altering distance and common fixed points for hybrid mappings under implicit relations and applications , Annales Mathematicae Silesianae: Vol. 28 (2014)
Anita Tomar, Meena Joshi, Results in strongly minihedral cone and scalar weighted cone metric spaces and applications , Annales Mathematicae Silesianae: Vol. 35 No. 2 (2021)
Mohamed Akkouchi, Valeriu Popa, Altering distances and fixed point results for tangential hybrid pairs of mappings , Annales Mathematicae Silesianae: Vol. 26 (2012)
Hakima Bouhadjera, A unique common fixed point for an infinity of set-valued maps , Annales Mathematicae Silesianae: Vol. 32 (2018)
Kushal Roy, Sayantan Panja, Mantu Saha, Zoran D. Mitrović, Some fixed point theorems via combination of weak contraction and Caristi contractive mapping , Annales Mathematicae Silesianae: Vol. 35 No. 2 (2021)
Valeriu Popa, A general fixed point theorem for two pairs of absorbing mappings in Gp-metric spaces , Annales Mathematicae Silesianae: Vol. 34 No. 2 (2020)
Poom Kumam, Muhammad Sarwar, Mian Bahadur Zada, Fixed point results satisfying rational type contractive conditions in complex valued metric spaces , Annales Mathematicae Silesianae: Vol. 30 (2016)
Mohammad Asim, Mohammad Imdad, Fixed point and best proximity point results in PIV-S-metric spaces , Annales Mathematicae Silesianae: 2024: Online First

1 2 3 4 5 6 7 8 9 10 > >>

You may also start an advanced similarity search for this article.

References

1. Banach S., Sur les operations dans les ensembles abstraits et leur applications aux equations integrales, Fund. Math. 3 (1922), 133–181.
2. De Blassi F.S., Myjak J., Sur la porosite des contractions sans point fixe, C. R. Math. Acad. Sci. Paris 308 (1989), 51–54.
3. Browder F.E., Petrysyn W.V., The solution by iteration of nonlinear functional equation in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 571–576.
4. Ćirić Lj.B., On some maps with a nonunique fixed points, Publ. Inst. Math. (Beograd) 13(31) (1974), 52–58.
5. Ćirić Lj.B., Generalized contractions and fixed point theorems, Publ. Inst. Math. (Beograd) 12(26) (1971), 19–26.
6. Ćirić Lj.B., Fixed points of asymptotically regular mappings, Math. Commun. 10 (2005), 111–114.
7. Guay M.D., Singh K.L., Fixed points of asymptotically regular mappings, Mat. Vesnik 35 (1983), 101–106.
8. Kincses J., Totik V., Theorems and counter-examples on contractive mappings, Math. Balkanica 4 (1990), 69–90.
9. Lahiri B.K., Das P., Well-posednes and porosity of certain classes of operators, Demonstratio Math. 38 (2005), 170–176.
10. Park S., On general contractive-type conditions, J. Korean Math. Soc. 17 (1980), 131–140.
11. Popa V., Fixed point theorems for implicit contractive mappings, Stud. Cercet. Stiint. Ser. Mat. Univ. Bacau 7 (1997), 129–133.
12. Popa V., Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32 (1999), 157–163.
13. Popa V., A general fixed point theorem for weakly compatible mappings in compact metric spaces, Turk. J. Math. 25 (2001), 465–474.
14. Popa V., Well Posedness of Fixed Point Problem in Orbitally Complete Metric Spaces, Stud. Cercet. Stiint. Ser. Mat. Univ. Bacau 16 (2006), Supplement. Proceedings of ICMI 45, Bacău, Sept. 18-20, 2006, pp. 209–214.
15. Popa V., Well Posedness of Fixed Point Problem in Compact Metric Spaces, Bul. Univ. Petrol-Gaze Ploies. Ser. Mat. Inf. Fiz. 60 (2008), no 1, 1–4.
16. Reich S., Zaslavski A.J., Well-posedness of fixed point problems, Far East J. Math. Sci. (FJMS) Special volume 2001, Part III, pp. 393–401.
17. Rhoades B.E., A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 26 (1971), 255–290.
18. Rhoades B.E., A collection of contractive definitions, Math. Sem. Notes 7 (1979), 229–235.
19. Sharma P.L., Yuel A.K., Fixed point theorems under asymptotic regularity at a point, Math. Sem. Notes 35 (1982), 181–190.
20. Tasković M.R., Some new principles in fixed point theory, Math. Japon. 35 (1990), 645–666.
21. Turkoglu D., Ozer O., Fisher B., Fixed point theorems for T-orbitally complete spaces, Stud. Cercet. Stiint. Ser. Mat. Univ. Bacau 9 (1999), 211–218. Google Scholar

Vol. 23 (2009)
Published: 2009-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

Submit