On the existence of a fuzzy integral equation of Urysohn-Volterra type
Mohamed Abdalla Darwish
Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 28 (2008), p. 75-82 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:271134 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1095,
     author = {Mohamed Abdalla Darwish},
     title = {On the existence of a fuzzy integral equation of Urysohn-Volterra type},
     journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
     volume = {28},
     year = {2008},
     pages = {75-82},
     zbl = {1178.45006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1095}
}

Mohamed Abdalla Darwish. On the existence of a fuzzy integral equation of Urysohn-Volterra type. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 28 (2008) pp. 75-82. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1095/

[000] [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. | Zbl 1164.34333

[001] [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. | Zbl 1152.45006

[002] [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.

[003] [4] D. Dubois and H. Parde, Towards fuzzy differential calculus, Part 1. Integraation of fuzzy mappings, Fuzzy Sets and Systems 8 (1982), 1-17.

[004] [5] D. Dubois and H. Parde, Towards fuzzy differential calculus, Part 2. Integraation of fuzzy mappings, Fuzzy Sets and Systems 8 (1982), 105-116.

[005] [6] J. Dugundji and A. Granas, Fixed Point Theory, Monografie Mathematyczne, PWN, Warsaw, 1982.

[006] [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. | Zbl 0949.65137

[007] [8] R. Goetschel and W. Voxman, Elementary Calculus, Fuzzy Sets and Systems 18 (1986), 31-43. | Zbl 0626.26014

[008] [9] O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems 24 (1987), 301-317. | Zbl 0646.34019

[009] [10] J. Mordeson and W. Newman, Fuzzy integral equations, Information Sciences 87 (1995), 215-229. | Zbl 0871.45002

[010] [11] S. Nanda, On integration of fuzzy mappings, Fuzzy Sets and Systems 32 (1989), 95-101. | Zbl 0671.28009

[011] [12] J.Y. Park and J.U. Jeong, A note on fuzzy integral equations, Fuzzy Sets and Systems 108 (1999), 193-200. | Zbl 0947.45001

[012] [13] M.L. Puri and D.A. Ralescu, Fuzzy random variables, J. Math. Anal. Appl. 114 (1986), 409-422. | Zbl 0592.60004

[013] [14] P.V. Subrahmanyam and S.K. Sudarsanam, A note on fuzzy Volterra integral equations, Fuzzy Sets and Systems 81 (1996), 237-240. | Zbl 0884.45002