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2008 | 28 | 1 | 75-82
Tytuł artykułu

On the existence of a fuzzy integral equation of Urysohn-Volterra type

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present an existence theorem for integral equations of Urysohn-Volterra type involving fuzzy set valued mappings. A fixed point theorem due to Schauder is the main tool in our analysis.
Twórcy
  • Department of Mathematics, Faculty of Science, Alexandria University (Damanhour Branch), 22511 Damanhour, Egypt
Bibliografia
  • [1] A. Arara and M. Benchohra, Fuzzy solutions for boundary value problems with integral boundary conditions, Acta Math. Univ. Comenianae, LXXV (1) (2006), 119-126.
  • [2] M. Benchohra and M.A. Darwish, Existence and uniqueness theorem for fuzzy integral equation of fractional order, Commun. Appl. Anal. 12 (1) (2008), 13-22.
  • [3] M.A. Darwish, On maximal and minimal solutions of fuzzy integral equation of Urysohn type, Accepted for publication in Int. Journal of Math. Analysis, 2006.
  • [4] D. Dubois and H. Parde, Towards fuzzy differential calculus, Part 1. Integraation of fuzzy mappings, Fuzzy Sets and Systems 8 (1982), 1-17.
  • [5] D. Dubois and H. Parde, Towards fuzzy differential calculus, Part 2. Integraation of fuzzy mappings, Fuzzy Sets and Systems 8 (1982), 105-116.
  • [6] J. Dugundji and A. Granas, Fixed Point Theory, Monografie Mathematyczne, PWN, Warsaw, 1982.
  • [7] M. Friedman, Ma Ming and A. Kandel, Solutions to fuzzy integral equations with arbitrary kernels, Internat. J. Approx. Reason. 20 (3) (1999), 249-262.
  • [8] R. Goetschel and W. Voxman, Elementary Calculus, Fuzzy Sets and Systems 18 (1986), 31-43.
  • [9] O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems 24 (1987), 301-317.
  • [10] J. Mordeson and W. Newman, Fuzzy integral equations, Information Sciences 87 (1995), 215-229.
  • [11] S. Nanda, On integration of fuzzy mappings, Fuzzy Sets and Systems 32 (1989), 95-101.
  • [12] J.Y. Park and J.U. Jeong, A note on fuzzy integral equations, Fuzzy Sets and Systems 108 (1999), 193-200.
  • [13] M.L. Puri and D.A. Ralescu, Fuzzy random variables, J. Math. Anal. Appl. 114 (1986), 409-422.
  • [14] P.V. Subrahmanyam and S.K. Sudarsanam, A note on fuzzy Volterra integral equations, Fuzzy Sets and Systems 81 (1996), 237-240.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1095
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