Common fixed point theorems in connection with two weakly compatible mappings in menger space with bicomplex-valued metric | ||
| Electronic Journal of Mathematical Analysis and Applications | ||
| Volume 12, Issue 1, January 2024, Pages 1-10 PDF (469.97 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/ejmaa.2024.243997.1087 | ||
| Authors | ||
| Sarmila Bhattacharyya* 1; Chinmay Biswas2; Tanmay Biswas3 | ||
| 1Department of Mathematics, Netaji Mahavidyalaya, P.O.- Arambagh, Dist.-Hooghly, PIN-712601, West Bengal, India. | ||
| 2Department of Mathematics, Nabadwip Vidyasagar College, Nabadwip, Dist.- Nadia, PIN-741302, West Bengal, India. | ||
| 3Rajbari, 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 | ||
| Probabilistic metric spaces; weakly compatible mappings; (CLRg) property; property (E.A); common fixed point | ||
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