Fixed point theorems in complex valued metric spaces

Singh, Naval; Singh, Deepak; Badal, Anil; Joshi, Vishal

doi:10.1016/j.joems.2015.04.005

Fixed point theorems in complex valued metric spaces

Authors

¹ Govt. Science and Commerce College, Benazeer, Bhopal, Madhya Pradesh, India

² Department of Applied Sciences, NITTTR, Ministry of HRD, Govt. of India, Bhopal, Madhya Pradesh 462002, India

³ Department of Mathematics, Barkatullah University, Bhopal, Madhya Pradesh, India

⁴ Department of Mathematics, Jabalpur Engineering College, Jabalpur, Madhya Pradesh, India

10.1016/j.joems.2015.04.005

Abstract

The aim of this paper is to establish and prove several results on common fixed point
for a pair of mappings satisfying more general contraction conditions portrayed by rational expres-
sions having point-dependent control functions as coefficients in complex valued metric spaces. Our
results generalize and extend the results of Azam et al. (2011) [1], Sintunavarat and Kumam (2012)
[2], Rouzkard and Imdad (2012) [3], Sitthikul and Saejung (2012) [4] and Dass and Gupta (1975)
[5]. To substantiate the authenticity of our results and to distinguish them from existing ones, some
illustrative examples are also furnished.

Keywords