Common fixed point theorems for converse commuting mappings in bicomplex valued metric spaces. (English) Zbl 1491.54068
Summary: The main purpose of this paper is to prove some common fixed point theorems for converse commuting self-maps for non-complete bicomplex valued metric spaces. Our results are the generalisations of the results of S. Chauhan and H. Sahper [J. Oper. 2013, Article ID 391474, 5 p. (2013; Zbl 1300.54063)] and J. Kumar et al. [“Common fixed point theorem for con-verse commuting maps in complex valued metric spaces”, Int. J. Math. Arch. 5, No. 6, 215–220 (2014)]. Moreover, some concepts of J. Choi et al., proved some fixed point theorems in connection with two weakly compatible mappings in bicomplex valued metric spaces published in [Honam Math. J. 39, No. 1, 115–126 (2017; Zbl 1376.30035)] and I. H. Jebril et al., proved common fixed point theorems under rational contractions for a pair of mappings in bicomplex valued metric spaces published in [“Common fixed point theorems under rational contractions for a pair of mappings in bicomplex valued metric spaces”, J. Interdisc. Math. 22, No. 7, 1071–1082 (2019; doi:10.1080/09720502.2019.1709318)] are used here.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
References:
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