Some common fixed point theorems for selfmappings satisfying two contractive conditions of integral type in a uniform space
Memudu Olatinwo
Open Mathematics, Tome 6 (2008), p. 335-341 / Harvested from The Polish Digital Mathematics Library

In this paper, we establish some common fixed point theorems for selfmappings of a uniform space by employing both the concepts of an A-distance and an E-distance introduced by Aamri and El Moutawakil [1] and two contractive conditions of integral type. Our results are generalizations and extensions of the classical Banach’s fixed point theorem of [2, 3, 19], some results of Aamri and El Moutawakil [1], Theorem 2.1 of Branciari [5] as well as a result of Jungck [7].

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:269325
@article{bwmeta1.element.doi-10_2478_s11533-008-0023-y,
     author = {Memudu Olatinwo},
     title = {Some common fixed point theorems for selfmappings satisfying two contractive conditions of integral type in a uniform space},
     journal = {Open Mathematics},
     volume = {6},
     year = {2008},
     pages = {335-341},
     zbl = {1161.54023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0023-y}
}
Memudu Olatinwo. Some common fixed point theorems for selfmappings satisfying two contractive conditions of integral type in a uniform space. Open Mathematics, Tome 6 (2008) pp. 335-341. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0023-y/

[1] Aamri M., El Moutawakil D., Common fixed point theorems for E-contractive or E-expansive maps in uniform spaces, Acta Math. Acad. Paedagog. Nyházi. (N.S.), 2004, 20, 83–91 | Zbl 1064.54504

[2] Berinde V., A priori and a posteriori error estimates for a class of ϕ-contractions, Bulletins for Applied & Computing Mathematics, 1999, 183–192

[3] Berinde V., Iterative approximation of fixed points, Editura Efemeride, Baia Mare, 2002

[4] Bourbaki N., Éléments de Mathématique, Fas. II. Livre III: Topologie Générale (Chapitre 1: Structures topologiques), (Chapter 2: Structures uniformes), Quatrième édition. Actualités Scientifiques et Industrielles, No. 1142, Hermann, Paris, 1965

[5] Branciari A., A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 2002, 29, 531–536 http://dx.doi.org/10.1155/S0161171202007524 | Zbl 0993.54040

[6] Jachymski J., Fixed point theorems for expansive mappings, Math. Japon., 1995, 42, 131–136 | Zbl 0845.47044

[7] Jungck G., Commuting mappings and fixed points, Amer. Math. Monthly, 1976, 83, 261–263 http://dx.doi.org/10.2307/2318216 | Zbl 0321.54025

[8] Kada O., Suzuki T., Takahashi W., Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon., 1996, 44, 381–391 | Zbl 0897.54029

[9] Kang S.M., Fixed points for expansion mappings, Math. Japon., 1993, 38, 713–717 | Zbl 0854.54038

[10] Olatinwo M.O., Some common fixed point theorems for selfmappings in uniform space, Acta Math. Acad. Paedagog. Nyházi. (N.S.), 2007, 23, 47–54

[11] Olatinwo M.O., Some existence and uniqueness common fixed point theorems for selfmappings in uniform space, Fasc. Math., 2007, 38, 87–95 | Zbl 1145.54325

[12] Olatinwo M.O., On some common fixed point theorems of Aamri and El Moutawakil in uniform spaces, Applied Mathematics E-Notes, to appear | Zbl 1154.54317

[13] Rhoades B.E., A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 1977, 226, 257–290 http://dx.doi.org/10.2307/1997954 | Zbl 0365.54023

[14] Rhoades B.E., Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 2003, 63, 4007–4013 http://dx.doi.org/10.1155/S0161171203208024 | Zbl 1052.47052

[15] Rodriguez-Montes J., Charris J.A., Fixed points for W-contractive or W-expansive maps in uniform spaces: toward a unified approach, Southwest J. Pure Appl. Math., 2001, 1, 93–101 | Zbl 0985.54036

[16] Rus I.A., Generalized contractions and applications, Cluj University Press, Cluj-Napoca, 2001

[17] Rus I.A., Petruşel A., Petruşel G., Fixed point theory 1950–2000 Romanian contributions, House of the Book of Science, Cluj Napoca, 2002 | Zbl 1005.54037

[18] Wang S.Z., Li B.Y., Gao Z.M., Iseki K., Some fixed point theorems on expansion mappings, Math. Japon., 1984, 29, 631–636 | Zbl 0554.54023

[19] Zeidler E., Nonlinear functional analysis and its applications I. Fixed-point theorems, Springer-Verlag, New York, 1986 | Zbl 0583.47050