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

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2008)

- Volume: 28, Issue: 1, page 75-82
- ISSN: 1509-9407

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topMohamed Abdalla Darwish. "On the existence of a fuzzy integral equation of Urysohn-Volterra type." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 28.1 (2008): 75-82. <http://eudml.org/doc/271134>.

@article{MohamedAbdallaDarwish2008,

abstract = {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.},

author = {Mohamed Abdalla Darwish},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {fuzzy integral equation; Urysohn-Volterra; Hausdorff metric; Schauder fixed point theorem; Urysohn-Volterra integral equation},

language = {eng},

number = {1},

pages = {75-82},

title = {On the existence of a fuzzy integral equation of Urysohn-Volterra type},

url = {http://eudml.org/doc/271134},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Mohamed Abdalla Darwish

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

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2008

VL - 28

IS - 1

SP - 75

EP - 82

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/271134

ER -

## References

top- [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. Zbl1164.34333
- [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. Zbl1152.45006
- [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. Zbl0949.65137
- [8] R. Goetschel and W. Voxman, Elementary Calculus, Fuzzy Sets and Systems 18 (1986), 31-43. Zbl0626.26014
- [9] O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems 24 (1987), 301-317. Zbl0646.34019
- [10] J. Mordeson and W. Newman, Fuzzy integral equations, Information Sciences 87 (1995), 215-229. Zbl0871.45002
- [11] S. Nanda, On integration of fuzzy mappings, Fuzzy Sets and Systems 32 (1989), 95-101. Zbl0671.28009
- [12] J.Y. Park and J.U. Jeong, A note on fuzzy integral equations, Fuzzy Sets and Systems 108 (1999), 193-200. Zbl0947.45001
- [13] M.L. Puri and D.A. Ralescu, Fuzzy random variables, J. Math. Anal. Appl. 114 (1986), 409-422. Zbl0592.60004
- [14] P.V. Subrahmanyam and S.K. Sudarsanam, A note on fuzzy Volterra integral equations, Fuzzy Sets and Systems 81 (1996), 237-240. Zbl0884.45002

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