Fixed Point Theorem in \(G\)-Metric Space for Auxiliary Functions




fixed point, auxiliary functions, G-metric space


In this paper, fixed point results satisfying generalized contractive condition with new auxiliary functions are proved in \(G\)-metric spaces.


Download data is not yet available.


M. A. Alghamdi and E. Karapınar, (G)-(beta)-(psi)-contractive type mappings and related fixed point theorems, Journal of Inequalities and Applications 2013 (2013), Article number: 70, DOI: 10.1186/1029-242X-2013-70.

A. H. Ansari, Note on (phi)-(psi) contractive type mappings and related fixed point, Proceedings of the 2nd Regional Conference on Mathematics and Applications, Payame Noor University, Iran, 2014, pp. 377 – 380.

A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, International Journal of Mathematics and Mathematical Sciences 29 (2002), Article ID 641824, 531 – 536, DOI: 10.1155/S0161171202007524.

B. C. Dhage, Generalized metric spaces and mappings with fixed point, Bulletin of the Calcutta Mathematical Society 84 (1982), 329 – 336.

B. C. Dhage, Generalized metric spaces and topological structure I, Analele Stiintifice Ale Universitatii “Al.I.Cuza” Iasi 46(1) (2000), 3 – 24, URL:

G. Jungck, Common fixed points for non-continuous non-self mappings on non-metric spaces, Far East Journal of Mathematical Sciences 4(1996), 199 – 212.

Z. Mustafa, A New Structure for Generalized Metric Spaces With Applications to Fixed Point Theory, Ph.D. Thesis, The University of Newcastle, Australia (2005).

Z. Mustafa, H. Obiedat and F. Awawdeh, Some fixed point theorems for mappings on complete G-metric spaces, Fixed Point Theory and Applications 2008(2008), Article ID 189870, 10 pages, DOI: 10.1155/2008/189870.

Z. Mustafa and B. Sims, A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis 7(2) (2006), 289 – 297, URL:

Z. Mustafa and B. Sims, Some remarks concerning D-metric spaces, Proceedings of the International Conference on Fixed Point Theory and Applications, Valencia, Spain, July 2003, pp. 189 – 198, URL:

W. Shatanawi, Fixed point theory for contractive mappings satisfying (varphi)-maps in (G)-metric spaces, Fixed Point Theory and Applications 2010(2010), Article ID 181670, 9 pages, DOI: 10.1155/2010/181650.

W. Sintunavarat and P. Kumam, Common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space, Journal of Applied Mathematics 2011(2011), Article ID 637958, 14 pages, DOI: 10.1155/2011/637958.




How to Cite

Bhardwaj, P., & Kumar, M. . (2021). Fixed Point Theorem in \(G\)-Metric Space for Auxiliary Functions. Communications in Mathematics and Applications, 12(4), 795–802.



Research Article