On the existence of a fuzzy integral equation of Urysohn-Volterra type
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 28 (2008) no. 1, pp. 75-82.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: fuzzy integral equation, Urysohn-Volterra, Hausdorff metric, Schauder fixed point theorem
@article{DMDICO_2008_28_1_a2,
     author = {Darwish, Mohamed},
     title = {On the existence of a fuzzy integral equation of {Urysohn-Volterra} type},
     journal = {Discussiones Mathematicae. Differential Inclusions, Control and Optimization},
     pages = {75--82},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {2008},
     zbl = {1178.45006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMDICO_2008_28_1_a2/}
}
TY  - JOUR
AU  - Darwish, Mohamed
TI  - On the existence of a fuzzy integral equation of Urysohn-Volterra type
JO  - Discussiones Mathematicae. Differential Inclusions, Control and Optimization
PY  - 2008
SP  - 75
EP  - 82
VL  - 28
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMDICO_2008_28_1_a2/
LA  - en
ID  - DMDICO_2008_28_1_a2
ER  - 
%0 Journal Article
%A Darwish, Mohamed
%T On the existence of a fuzzy integral equation of Urysohn-Volterra type
%J Discussiones Mathematicae. Differential Inclusions, Control and Optimization
%D 2008
%P 75-82
%V 28
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMDICO_2008_28_1_a2/
%G en
%F DMDICO_2008_28_1_a2
Darwish, Mohamed. On the existence of a fuzzy integral equation of Urysohn-Volterra type. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 28 (2008) no. 1, pp. 75-82. http://geodesic.mathdoc.fr/item/DMDICO_2008_28_1_a2/

[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.