Czasopismo
2013
|
Vol. 46, nr 2
|
373--382
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
In 2006, I. Beg and M. Abbas have studied the existence of coincidence and common fixed points for two mappings satisfying a weak contractive condition. Their results were extended in 2008 by A. Azam and M. Shakeel to the case of three mappings. Recently M. Abbas and D. Dorić employed the contractive conditions introduced in [Q. Zhang and Y. Song, Fixed point theory for generalized ϕ-weak contraction, Appl. Math. Lett. 22(2009), 75-78] and [D. Dorić, Common fixed point for generalized (...)-weak contractions, Appl. Math. Lett. 22 (2009), 1896–1900] to prove a common fixed point theorem for four mappings satisfying generalized weak contractive condition (see Filomat 24:2 (2010), 1–10). In this paper, we generalize this theorem by using the concept of common property (E.A). Our result generalizes and unifies several existing results involving generalized weak contractive conditions. We study also well-posedness of a related fixed point problem.
Czasopismo
Rocznik
Tom
Strony
373--382
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
- Université Cadi Ayyad Faculté des Sciences-Semlalia Département de Mathématiques Av. Prince My Abdellah, Bp. 2390 Marrakech, Maroc, Morocco, akkouchimo@yahoo.fr
Bibliografia
- [1] M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, Math. Anal. Appl. 270 (2002), 181–188.
- [2] M. Abbas, D. Dorić, Common fixed point theorem for four mappings satisfying generalized weak contractive condition, Filomat 24(2) (2010), 1–10.
- [3] A. Azam, M. Shakeel, Weakly contractive maps and common fixed points, Mat. Vesnik 60(4) (2008), 101–106.
- [4] Ya. I. Alber, S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces, New Results in Operator Theory and Its Applications (I. Gohberg and Yu. Lyubich, eds.), Oper. Theory Adv. Appl., vol. 98, Birkhuser, Basel, 1997, pp. 7–22.
- [5] S. Banach, Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales, Fund. Math. 3 (1922), 133–181.
- [6] I. Beg, M. Abbas, Fixed points and best approximation in Menger convex metric spaces, Archivum Mathematicum 41 (2005), 389–397.
- [7] I. Beg, M. Abbas, Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed Point Theory Appl. 2006 (2006), 1–7.
- [8] I. Beg, M. Abbas, Fixed point theorems for weakly inward multivalued maps on a convex metric space, Demonstratio Math. 39 (2006), 149–160.
- [9] I. Beg, A. Azam, Common fixed points for commuting and compatible maps, Discussiones Mathematicae, Differential Inclusions 16(2) (1996), 121–135.
- [10] F. S. De Blassi, J. Myjak, Sur la porosite des contractions sans point fixe, Comptes Rendus Academie Sciences Paris 308 (1989), 51–54.
- [11] D. Dorić, Common fixed point for generalized (…)-weak contractions, Appl. Math. Lett. 22 (2009), 1896–1900.
- [12] G. Jungck, Common fixed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc. 103(3) (1988), 977–983.
- [13] G. Jungck, B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (1998), 227–238.
- [14] T. Kamran, Coincidence and fixed points for hybrid strict contractions, J. Math. Anal. Appl. 299 (2004), 235–241.
- [15] H. Kaneko, S. Sessa, Fixed point theorems for compatible multi-valued and single-valued mappings, Internat. J. Math. Math. Sci. 12(2) (1989), 257–262.
- [16] B. K. Lahiri, P. Das, Well-posednes and porosity of certain classes of operators, Demonstratio Math. 38 (2005), 170–176.
- [17] Y. Liu, J. Wu, Z. Li, Common fxed points of single-valued and multi-valued maps, Internat. J. Math. Math. Sci. 19 (2005), 3045–3055.
- [18] R. P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188(2) (1994), 436–440.
- [19] V. Popa, Well-posedness of fixed point problem in orbitally complete metric spaces, Stud. Cerc. St. Ser. Mat. Univ. 16 (2006), Supplement. Proceedings of ICMI 45, Bacˇau, Sept. 18–20, 2006, pp. 209–214.
- [20] V. Popa, Well-posedness of fixed point problem in compact metric spaces, Bul. Univ. Petrol-Gaze, Ploiesti, Sec. Mat. Inform. Fiz. 60(1) (2008), 1–4.
- [21] S. Reich, A. J. Zaslavski, Well-posednes of fixed point problems, Far East J. Math. Sci., Special volume 2001, Part III, pp. 393–401, 2001.
- [22] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47(3) (2001), 2683–2693.
- [23] S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Institut Math. Publications, Nouvelle série 32(46) (1982), 149–153.
- [24] Q. Zhang, Y. Song, Fixed point theory for generalized ϕ-weak contractions, Appl. Math. Lett. 22 (2009), 75–78.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-8f1a92f3-b812-47e4-875c-e0def9f6e64c