Unified implicit common fixed point theorems under non-negative complex valued functions satisfying the identity of indiscernible
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Authors
Deepak Singh
- Department of Applied Sciences, NITTTR, Under Ministry of HRD, Govt. of India, Bhopal, (M.P.) 462002, India.
Vishal Joshi
- Department of Applied Mathematics, Jabalpur Engineering College, Jabalpur, (M.P.), India.
Mohammad Imdad
- Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India.
Poom Kumam
- Department of Mathematics & Theoretical and Computational Science (TaCS) Center, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand.
- China Medical University, No. 91, Hsueh-Shih Road, Taichung, Taiwan.
Abstract
In this paper, we consider a non-negative complex valued function satisfying the identity of indiscernible
and utilize the same to prove some common fixed point theorems for two pairs of non-vacuously weakly compatible mappings satisfying an implicit relation having rational terms as its co-ordinates. Some illustrative
examples are also given which demonstrate the validity of the hypotheses of our results. In process, a host
of previously known results in the context of complex as well as real valued metric spaces are generalized
and improved.
Share and Cite
ISRP Style
Deepak Singh, Vishal Joshi, Mohammad Imdad, Poom Kumam, Unified implicit common fixed point theorems under non-negative complex valued functions satisfying the identity of indiscernible, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 2049--2069
AMA Style
Singh Deepak, Joshi Vishal, Imdad Mohammad, Kumam Poom, Unified implicit common fixed point theorems under non-negative complex valued functions satisfying the identity of indiscernible. J. Nonlinear Sci. Appl. (2016); 9(5):2049--2069
Chicago/Turabian Style
Singh, Deepak, Joshi, Vishal, Imdad, Mohammad, Kumam, Poom. "Unified implicit common fixed point theorems under non-negative complex valued functions satisfying the identity of indiscernible." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 2049--2069
Keywords
- Complex valued metric spaces
- non-vacuously weakly compatible mappings
- implicit relations
- coincidence point
- point of coincidence
- fixed point.
MSC
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