Geodesic
Quasi-Contractions on a Nonnormal Cone Metric Space
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 1, pp. 75-79.

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

Ilić and Rakočević [Appl. Math. Lett., 22:5 (2009), 728–731] proved a fixed point theorem for quasi-contractive mappings on cone metric spaces when the underlying cone is normal. Recently, Z. Kadelburg, S. Radenović, and V. Rakočević obtained a similar result without using the normality condition but only for a contractive constant $\lambda\in(0,1/2)$ [Appl. Math. Lett., 22:11 (2009), 1674–1679]. In this note, using a new method of proof, we prove this theorem for any contractive constant $\lambda \in (0,1)$.
Keywords: fixed point, cone metric space
Mots-clés : quasi-contraction. 
@article{FAA_2012_46_1_a7,
     author = {L. Gaji\'c and V. Rako\v{c}evi\'c},
     title = {Quasi-Contractions on a {Nonnormal} {Cone} {Metric} {Space}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {75--79},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a7/}
}
TY  - JOUR
AU  - L. Gajić
AU  - V. Rakočević
TI  - Quasi-Contractions on a Nonnormal Cone Metric Space
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2012
SP  - 75
EP  - 79
VL  - 46
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a7/
LA  - ru
ID  - FAA_2012_46_1_a7
ER  - 
%0 Journal Article
%A L. Gajić
%A V. Rakočević
%T Quasi-Contractions on a Nonnormal Cone Metric Space
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2012
%P 75-79
%V 46
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a7/
%G ru
%F FAA_2012_46_1_a7
L. Gajić; V. Rakočević. Quasi-Contractions on a Nonnormal Cone Metric Space. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 1, pp. 75-79. http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a7/

[1] M. Abbas, B. E. Rhoades, Appl. Math. Lett., 22:4 (2009), 511–515 | DOI | MR | Zbl

[2] C. D. Bari, P. Vetro, Rend. Circ. Mat. Palermo, 57:2 (2008), 279–285 | DOI | MR | Zbl

[3] Lj. B. Ćirić, Proc. Amer. Math. Sc., 45 (1974), 267–273 | MR

[4] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985 | MR | Zbl

[5] L.-G. Huang, X. Zhang, J. Math. Anal. Appl., 332:2 (2007), 1468–1476 | DOI | MR | Zbl

[6] D. Ilić, V. Rakočević, Appl. Math. Lett., 22:5 (2009), 728–731 | DOI | MR | Zbl

[7] G. Jungck, S. Radenović, S. Radojević, V. Rakočević, Fixed Point Theory and Applications, 2009, Art. ID 643840 | DOI | MR | Zbl

[8] Z. Kadelburg, S. Radenović, V. Rakočević, Appl. Math. Lett., 22:11 (2009), 1674–1679 | DOI | MR | Zbl