Priya Shahi, Jatinderdeep Kaur and S. S. Bhatia Res. Fixed Point Theory Appl. Volume 2018, Article ID 20187, 20 pages eISSN 2581-6047 Results in Fixed Point Theory and Applications RESEARCH ARTICLE Fixed point theorems for (α, φ)-contractive mappings of rational type in complex valued metric spaces with applications Priya Shahi ∗ , Jatinderdeep Kaur 1 and S. S.Bhatia 2 ∗,1,2 School of Mathematics and Computer Applications, Thapar University, Patiala, Punjab, India. Academic Editor: Abdul Latif Abstract: A very interesting approach in the theory of contractive mappings was recently given by Samet et al. (Nonlinear Anal. 75, 2012, 2154-2165) by using the concept of α-ψ contractive type mappings in metric spaces. The purpose of this paper is to give the generalized version of α-ψ contractive type mappings in complex valued metric spaces. For this, we define the notion of (α, φ)-contractive map- pings of rational type and obtain fixed point theorems for such mappings in the framework of complex valued metric spaces. This extends and subsumes the re- cent results of Azam et al. (Numerical Functional Analysis and optimization 32, 2011, 243-253) and Rouzkard and Imdad (Computers and Mathematics with Ap- plications 2012, doi:10.1016/j.camwa.2012.02.063) regarding common fixed point theorems in complex valued metric spaces. Also, we derive common coupled fixed point theorems in complete complex valued metric spaces. Our results gen- eralize many previously obtained results. Some examples are presented to verify the effectiveness and applicability of our main results. Towards the end, an ap- plication to integral equations has also been presented to support the usability of the obtained results. Keywords: Common fixed point; Contractive type mapping; Complex valued metric space; Coupled fixed point. MSC: 54H25, 47H10, 54E50. c  by the SUMA Publishing Group. DOI: 10.30697/rfpta-2018-7 *Corresponding author E-mail: priya.thaparian@gmail.com Received January 13, 2018; revised March 16, 2018; accepted March 18, 2018. This is an open access article under the CC BY license http://creativecommons.org/licenses/by/4.0/. 1