Mathematics and Statistics Vol. 10(6), pp. 1334 - 1339
DOI: 10.13189/ms.2022.100620
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Some Fixed Point Results in Bicomplex Valued Metric Spaces

Duduka Venkatesh ^*, V. Naga Raju
Department of Mathematics, Osmania University, Hyderabad, 500007, Telangana, India

ABSTRACT

Fixed points are also called as invariant points. Invariant point theorems are very essential tools in solving problems arising in different branches of mathematical analysis. In the present paper, we establish three unique common invariant point theorems using two self-mappings, four self-mappings and six self-mappings in the bicomplex valued metric space. In the first theorem, we generate a common invariant point theorem for four self-mappings by using weaker conditions such as weakly compatible, generalized contraction and property. Then, in the second theorem, we generate a common invariant point theorem for six self-mappings by using inclusion relation, generalized contraction, weakly compatible and commuting maps. Further, in the third theorem, we generate a common coupled invariant point for two self mappings using different contractions in the bicomplex valued metric space. The above results are the extention and generalization of the results of [11] in the Bicomplex metric space. Moreover, we provide an example which supports the results.

KEYWORDS
Bicomplex Valued Metric Space, Common Fixed Point, Coupled Fixed Point, CLR Property, Weakly Compatible Mappings

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Duduka Venkatesh , V. Naga Raju , "Some Fixed Point Results in Bicomplex Valued Metric Spaces," Mathematics and Statistics, Vol. 10, No. 6, pp. 1334 - 1339, 2022. DOI: 10.13189/ms.2022.100620.

(b). APA Format:
Duduka Venkatesh , V. Naga Raju (2022). Some Fixed Point Results in Bicomplex Valued Metric Spaces. Mathematics and Statistics, 10(6), 1334 - 1339. DOI: 10.13189/ms.2022.100620.