**Title:** On a Common Fixed Point Theorem in Bicomplex Valued *b*-metric Space

**Montes Taurus J. Pure Appl. Math.** / ISSN: 2687-4814

**Article ID:** MTJPAM-D-20-00017; **Volume 3 / Issue 3 / Year 2021 (Special Issue)**, Pages 358-366

**Document Type:** Research Paper

**Author(s):** Sanjib Kumar Datta ^{a} , Dipankar Pal ^{b} , Rakesh Sarkar ^{c} , Arghyatanu Manna ^{d}

^{a}Department of Mathematics, University of Kalyani, P.O.: Kalyani, Dist.: Nadia, PIN-741235, West Bengal, India. Ph. no.-8017105978

^{b}Department of Mathematics, Prof. Syed Nurul Hasan College, P.O.: Farakka Barrage, Dist.: Murshidabad, PIN-742212, West Bengal, India. Ph.no.-9153837959

^{c}Department of Mathematics, Gour Mahavidyalaya, P.O.: Mangalbari, Dist.: Malda, PIN-732142, West Bengal, India. Ph. no.-9733608224

^{d}Mousini Co-operative High School(H.S.), Bagdanga, Fraserganj Coastral, Kakdwip,South 24 Parganas, PIN-743357. Ph.no.-8599972619

Received: 8 July 2020, Accepted: 15 April 2021, Published: 25 April 2021.

**Corresponding Author:** Sanjib Kumar Datta (Email address: sanjibdatta05@gmail.com)

**Full Text:** PDF

**Abstract**

The main purpose of this paper is to investigate a common fixed point theorem in bicomplex valued *b*-metric space satisfying some rational inequalities for two pairs of weakly compatible self contracting mappings and to extend the result obtained by Azam et al.[1]. Our result is the generalisation of the result of Mitra[21] and the application of Banach contraction principle. Also we use the concepts of Choi et al.[11] and Datta et al.[15]

**Keywords:** Common fixed point, Contractive type mapping, Bicomplex valued metric space, Bicomplex valued *b*-metric space

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