Document Type : Regular research papers
Authors
1
Department of Mathematics, Netaji Mahavidyalaya, P.O.- Arambagh, Dist.-Hooghly, PIN-712601, West Bengal, India.
2
Department of Mathematics, Nabadwip Vidyasagar College, Nabadwip, Dist.- Nadia, PIN-741302, West Bengal, India.
3
Rajbari, Rabindrapally, R. N. Tagore Road, P.O.-Krishnagar, P.S.-Katwali, Dist-Nadia, PIN- 741101, West Bengal, India.
Abstract
It is well-known that the fixed point theory plays a very important role in theory and applications. In 2017, Choi et al. [4] introduced the notion of bicomplex valued metric spaces (bi-CVMS) and established common fixed point results for weakly compatible mappings. On the other hand, in 1942, K. Menger [14] initiated the study of probabilistic metric spaces where he replaced the distance function $d(x,y)$ by distribution function $Fx,y(t)$, where the value of $Fx,y(t)$ is interpreted as the probability that the distance between $x$ and $y$ be less than $t$, $t>0$. In this paper, we have used bicomplex-valued metric on a set. We have taken $Fx,y(t)$ as the probability that norm of the distance between $x$ and $y$ be less than $t$, i.e., $||d(x,y)||<t$, $t>0$ and initiated menger space with bicomplex valued metric. We also aim to prove certain common fixed point theorems for a pair of weakly compatible mappings satisfying (CLRg) or (E.A) property in this space.
Keywords
Main Subjects
)
View on SCiNiTO