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

• Autorzy: Mohamed Abdalla Darwish
• 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.

Słowa kluczowe

EN

fuzzy integral equation; Urysohn-Volterra; Hausdorff metric; Schauder fixed point theorem

Kategorie tematyczne

• 45G10: Other nonlinear integral equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2008
• Tom: 28
• Numer: 1
• Strony: 75-82

Daty

wydano

2008

otrzymano

2006-10-23

Twórcy

autor

Mohamed Abdalla Darwish

• 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.

Identyfikatory

DOI

10.7151/dmdico.1095