The purpose of this paper is to introduce and discuss the concepts of G-best approximation and a 0 -orthogonality in the theory of G-metric spaces. We consider the relationship between these concepts and the dual X and obtain some results on subsets of G-metric spaces similar to normed spaces.
Similar content being viewed by others
References
Z. Mustafa and B. Sims, “A new approach to generalized metric spaces,” J. Nonlin. Convex Anal., 7, No. 2, 289–297 (2006).
F. Mazaheri and F. M. Maalek Ghaini, “Quasi-orthogonality of the best approximant sets,” Nonlinear Anal., 65, 534–537 (2006).
H. Mazaheri and S. M. Moshtaghouion, “The orthogonality in the vector spaces,” Bull. Iran. Math. Soc., 35, No. 1, 119–127 (2009).
H. Mazaheri and S. M. Vaezpour, “Orthogonality and ε-orthogonality in Banach spaces,” Aust. J. Math. Anal. Appl., 2, No. 1, 1–5 (2005).
Author information
Authors and Affiliations
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 4, pp. 567–571, April, 2010.
Rights and permissions
About this article
Cite this article
Dehghan Nezhad, A., Mazaheri, H. New results in G-best approximation in G-metric spaces. Ukr Math J 62, 648–654 (2010). https://doi.org/10.1007/s11253-010-0377-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-010-0377-8