Research Article
Common Fixed Point Results in G-Metric Spaces and Applications
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 43 - Issue 11 |
| Published: April 2012 |
| Authors: Meenakshi Gugnani, Madhu Aggarwal, Renu Chugh |
10.5120/6151-8538
|
Meenakshi Gugnani, Madhu Aggarwal, Renu Chugh . Common Fixed Point Results in G-Metric Spaces and Applications. International Journal of Computer Applications. 43, 11 (April 2012), 38-42. DOI=10.5120/6151-8538
@article{ 10.5120/6151-8538,
author = { Meenakshi Gugnani,Madhu Aggarwal,Renu Chugh },
title = { Common Fixed Point Results in G-Metric Spaces and Applications },
journal = { International Journal of Computer Applications },
year = { 2012 },
volume = { 43 },
number = { 11 },
pages = { 38-42 },
doi = { 10.5120/6151-8538 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2012
%A Meenakshi Gugnani
%A Madhu Aggarwal
%A Renu Chugh
%T Common Fixed Point Results in G-Metric Spaces and Applications%T
%J International Journal of Computer Applications
%V 43
%N 11
%P 38-42
%R 10.5120/6151-8538
%I Foundation of Computer Science (FCS), NY, USA
Abstract
A common fixed point theorem using EA-property for four weakly compatible maps is obtained in the setting of G- metric spaces without exploiting the notion of continuity. Our results generalize the results of Abbas and Rhoades[7], and Manro et. al. [11]. Moreover, we show that these maps satisfy property R. Applications to certain intergral equations and functional equations are also obtained.
References
- Rhoades, B. E. and Abbas, M. , Maps satisfying generalized contractive condition of integral type for which F(T) = F(Tn), Int. J. of Pure and Applied Math. , vol. 45, No. 2 (2008), 225-231.
- Jungck, G. and Rhoades, B. E. , Fixed point for set valued functions without continuity, Indian J. Pure and Appl. Math. , 29(1998), 227-238.
- Jeong, G. S. and Rhoades, B. E. , Maps for which F(T) = F(Tn), Fixed point theory and applications, vol. 6, (2004), 71-105.
- Jeong, G. S. and Rhoades, B. E. , More maps for which F(T) = F(Tn), Demonstratio Mathematica, vol. XL, no. 3, (2007), 671-680.
- Altun, I. and Simsek, H. , Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory and Applications, Volume 2010, Article ID 6214469, (2010), 17 pages.
- Nieto, J. J. , An abstract monotone iterative technique, Nonlinear Analysis: Theory Methods and Applications, 28 (1997), 1923-1933.
- Abbas, M. and Rhoades, B. E. , Common fixed point results for noncommuting mappings without continuity in generalized metric spaces, Applied Math. and Comp. ,215 (2009), 262-269.
- Abbas, M. , Khan, S. H. and Nazir, T. Common fixed points of R-weakly commuting maps in generalized metric spaces, Fixed Point Theory and Appl. , Volume 2011 (41),(2011), 11 pages.
- Aamri, M. and Moutawakil, D. El. , Some new common fixed point theorems under strict contractive conditions , J. Math. Anal. Appl. , 270(2002), 181-188.
- Chugh, R. , Kadian, T. , Rani, A. and Rhoades, B. E. , Property P in G-metric spaces, Fixed Point Theory and App. , Volume 2010, Article ID 401684, (2010),12 pages.
- Manro, S. , Bhatia, S. S. and Kumar, S. , Expansion Mapping Theorems In G-metric spaces, Int. J. Contemp. Math. Sciences, Vol. 5, no. 51, (2010), 2529-2535.
- Singh, S. L. and Mishra, S. N. , Remarks on recent fixed point theorems, Fixed Point Theory and Appl. , Volume 2010, Article ID 452905,(2010), 18 pages.
- Singh, S. L. and Mishra, S. N. , Coincidence theorems for certain classes of hybrid contractions, Fixed Point Theory and Appl. , Vol. 2010, Article ID 898109, (2010), 14 pages.
- Mustafa, Z. , Obiedat, H. and Awawdeh, F. , Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory and Appl. , Vol. 2008, Article ID 189870,(2008), 12pages.
- Mustafa, Z. , and Sims, B. , A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis, vol. 7, no. 2, (2006), 289-297.
Index Terms
Keywords