| บทคัดย่อ |
Mongkolkeha et al. [6] proved two xed point theorems in modular metric spaces. Un-
fortunately there are many gaps in their proofs reported in [1, 4, 7]. Abdou and Khamsi [1]
gave some corrections with the regularity assumption. In this paper, we present three xed
point theorems in modular metric spaces without assuming the regularity as was the case
in Abdou and Khamsi [1].
References
[1] A. N. Abdou and M. A. Khamsi, Fixed point results of pointwise contractions in modular
metric spaces, Fixed Point Theory Appl. 2013 (2013), no. 163, 11 pp.
[2] V. V. Chistyakov, Modular metric spaces. I. Basic concepts, Nonlinear Anal. 72 (2010),
1{14.
[3] V. V. Chistyakov, Modular metric spaces. II. Application to superposition operators, Non-
linear Anal. 72 (2010), 15{30.
[4] H. Dehghan, Gordji M. Eshaghi and A. Ebadian, Comment on `Fixed point theorems for
contraction mappings in modular metric spaces, Fixed Point Theory and Applications,
doi:10.1186/1687-1812-2011-93, 9 pages' Fixed Point Theory Appl. 2012 (2012), no. 144,
3 pp.
[5] J. Martnez-Moreno, W. Sintunavarat and P. Kumam, Banach's contraction principle for
nonlinear contraction mappings in modular metric spaces, Bull. Malays. Math. Sci. Soc.
40 (2017), 335{344.
[6] C. Mongkolkeha, W. Sintunavarat and P. Kumam, Fixed point theorems for contraction
mappings in modular metric spaces, Fixed Point Theory Appl. 2011 (2011), 9 pp.
[7] C. Mongkolkeha, W. Sintunavarat and P. Kumam, Erratum to Fixed point theorems for
contraction mappings in modular metric spaces, Fixed Point Theory Appl. 2011, 2011: 93,
Fixed Point Theory Appl. 2012 (2012), 3 pp.
[8] H. Nakano, Modulared Semi-Ordered Linear Spaces, Maruzen Co., Ltd., Tokyo, 1950. |
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