A New Approach to G-Normed Spaces: Functionally Generalized Normed Spaces

A New Approach to G-Normed Spaces: Functionally Generalized Normed Spaces

In this paper, we introduce functionally generalized normed spaces as a generalization of G  metric spaces and normed spaces. Some constructions are described within this structure and some related results are obtained.

___

  • 7. Maddox, I. J.; Elements of functional analysis. Second edition. Cambridge University Press, Cambridge, 1988; pp. 242
  • 6. Fernandez, J. and Malviya, N.; Pseudo- G  metric spaces and pseudo- G  metric product spaces. South Asian Journal of Mathematics. 2013, 3 (1), 339-343.
  • 5. Gahler, S.; 2-Metrische Raume und ihre topologische struktur. (German) Mathematische Nachrichten. 1963, 26, 115-148.
  • 4. Shrivastava, R., Animesh, G. and Yadava, R. N.; Some mapping on G  Banach space. International Journal of Mathematical Science and Engineering Applied. 2011, 5 (IV), 245-260.
  • 3. Mohammedpour, A. and Shobe, N.; Stability of addi- tive mappings in generalized normed space, Tam- suiOxf. Jornal of Informatics and Mathematical Scien- ces. 2013, 29(2), 201-217.
  • 2. Dhage, B. C.; Generalized metric space and mapping with fixed point. Bulletin of the Calcutta Mathematical Society. 1992, 84, 329-336.
  • 1. Mustafa, Z. and Sims, B.; A new approach to generali- zed metric spaces, Journal of Nonlinear and Convex Analysis. 2006, 7(2), 289-297.