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AbstractIn this paper, we establish a solution to the following integral equation: 1u(t)=∫0TG(t,s)f(s,u(s))dsfor all t∈[0,T], where T>0, f:[0,T]×R→R and G:[0,T]×[0,T]→[0,∞) are continuous functions. For this purpose, we also obtain some auxiliary fixed point results which generalize, improve and unify some fixed point theorems in the literature.MSC:47H10, 54H25.

Existence of a solution of integral equations via fixed point theorem