Keywords and phrases: fixed point, common fixed point, Das and Gupta contraction, complex valued metric spaces.
Received: April 2, 2022; Accepted: May 12, 2022; Published: June 8, 2022
How to cite this article: Surendra Kumar Tiwari and Bindeshwari Sonant, Complex valued metric spaces for Das and Gupta contraction and fixed point and common fixed point theorems, JP Journal of Fixed Point Theory and Applications 17 (2022), 11-38.
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] A. Azam, B. Fisher and M. Khan, Common fixed-point theorems in complex value metric spaces, Numerical Functional Analysis and Optimization 32(3) (2011), 243-253. [2] F. Rouzkard and M. Imdad, Common fixed-point theorems in complex value metric spaces, Computers and Math. with Analysis 64 (2012), 1866-1874. [3] N. Soni and R. P. Dubey, New fixed point results in complex valued metric spaces, Journal of Computer and Mathematical Sciences 9(10) (2018), 1320 1325. [4] J. Azam Ahmad and P. Kumar, Common fixed point theorems for multi valued mapping in complex valued metric spaces, J. Inequal Appl. 2013 (2013), 578. [5] M. Abbas, M. Arshad and A. Azam, Fixed points of asymptotically regular mappings in complex valued metric spaces, Georgian Maths. J. 20(2) (2013), 213 221. [6] M. A. Kutbi, A. Azam, J. Ahmad and C. Bari Di, Some common coupled fixed point results for generalized contractions in complex-valued metric spaces, J. Appl. Math. 2013, Article ID 352927. [7] C. Klin-Cam and C. Suanoo, Some common fixed point theorems for generalized contractive type mapping an complex-valued metric spaces, Abstr. Appl. and 2013 (2013), Article ID 604215. [8] F. Rouzkard and M. Imdad, Some common fixed point theorems on complex value metric spaces, Comput. Math. Appl. 64(6) (2012), 1866-1874. [9] W. Sintunavarat and P. Kunmanr, Generalized common fixed point theorems in complex valued metrics spaces an applications, J. Inequd. App. 2012 (84), 2012. [10] W. Sintunavarat, Y. J. Cho and P. Kumam, Urysohn integral equations approach by common fixed points in complex-valued metric spaces, Adv. Difference Equ. 2013, 2013:49, 14 pp. [11] K. Sitthikul and S. Saejung, Some fixed point theorems in complex valued metric spaces, Fixed Point Theory Appl. 2012, 2012:189, 11 pp. [12] T. Senthil Kumar and R. Jahirhuss, and common fixed point Theorems per generalized contractive type mapping in complex- valued metric spaces, J. Math. Comp. Sci. 4 (2014), 639-648. [13] H. K. Nashine, M. Imdads and M. Hasan, Common fixed point theorems under rational contractions in complex-valued metric spaces, J. Nan. Linear. Sci. Appl. 7 (2014), 42-50. [14] B. S. Choudhary, N. Metiya and P. Konar, Fixed point results and rational type contraction in partially ordered complex-valued metric spaces, Bulletin of the Int. Math. Virtual Institute 5 (2015), 73-80. [15] S. U. Khan, M. Arshad, H. K. Nashine and M. Nazam, Some common fixed points of generalized contractive mappings a complex-valued metric spaces 5(1) (2017), 73-80. [16] G. S. Saluja, Fixed point theorems under rational contraction in complex valued metric spaces, Nonlinear Funct. Anal. Appl. 22(1) (2017), 209-216. [17] B. K. Das and S. Gupta, An extension of Banach contraction principle through rational expression, Indian Journal Pure Appl. Math. 6 (1975), 1455-1458. [18] V. W. A. Bryant, Remark on a fixed point theorem for iterated mappings, Amer. Math. Monthly 75 (1968), 399-400.
|