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

Mohamed Abdalla Darwish (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock-Kurzweil integrals

Aneta Sikorska-Nowak (2004)

Annales Polonici Mathematici

We prove some existence theorems for nonlinear integral equations of the Urysohn type x ( t ) = φ ( t ) + λ 0 a f ( t , s , x ( s ) ) d s and Volterra type x ( t ) = φ ( t ) + 0 t f ( t , s , x ( s ) ) d s , t I a = [ 0 , a ] , where f and φ are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock-Kurzweil integral.

On the Hammerstein equation in the space of functions of bounded ϕ -variation in the plane

Luis Azócar, Hugo Leiva, Jesús Matute, Nelson Merentes (2013)

Archivum Mathematicum

In this paper we study existence and uniqueness of solutions for the Hammerstein equation u ( x ) = v ( x ) + λ I a b K ( x , y ) f ( y , u ( y ) ) d y , x I a b : = [ a 1 , b 1 ] × [ a 2 , b 2 ] , in the space B V ϕ ( I a b ) of function of bounded total ϕ - variation in the sense of Riesz, where λ , K : I a b × I a b and f : I a b × are suitable functions.

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