Unified fixed point theorems for mappings in fuzzy metric spaces via implicit relations

Chauhan, Sunny; Imdad, Mohammad; Sintunavarat, Wutiphol; Shen, Yonghong

doi:10.1016/j.joems.2014.05.008

Unified fixed point theorems for mappings in fuzzy metric spaces via implicit relations

Document Type : Original Article

Authors

¹ Near Nehru Training Centre, H. No. 274, Nai Basti B-14, Bijnor 246 701, Uttar Pradesh, India

² b Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India

³ Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand

⁴ School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, PR China

10.1016/j.joems.2014.05.008

Abstract

In this paper, we prove some fixed point theorems for weakly compatible mappings in
fuzzy metric spaces employing common limit range property with implicit relations. We also furnish
some illustrative examples to support our main results. As an application to our main result, we
derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive
common fixed point theorems involving any finite number of mappings. Our results improve and
extend a host of previously known results including the ones contained in the paper of Gopal
et al. (2011).

Keywords