Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

Kutukcu S., Tuna A., Yakut A. T.

APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, vol.28, no.6, pp.799-809, 2007 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 6
  • Publication Date: 2007
  • Doi Number: 10.1007/s10483-007-0610-z
  • Journal Name: APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.799-809
  • Keywords: generalized contraction mapping, intuitionistic Menger space, intuitionistic Menger normed space, intuitionistic probabilistic bounded set, FUZZY METRIC-SPACES
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.