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An integral equation with modified argument. (English) Zbl 1073.45506

Using the work of I. A Rus [Comment. Math. Univ. Carol. 34, No. 4, 769–773 (1993; Zbl 0787.54045); Babes-Bolyai Univ. Fac. Math. Comput. Sci., Res. Semin. Prepr. 1996, No. 3, 3–36 (1996; Zbl 0906.47044)] and of J. Sotomayor [Bos. Soc. Bras. Mat. 4, No. 1, 55–59 (1973; Zbl 0337.34005)], a theorem of differentiability of the solution of the equation \[ x(t)=\int_a^bK(t,s,x(s),x(\varphi(s)))\, ds+g(t),\quad t\in[\alpha,\beta] \] is given.

MSC:

45G10 Other nonlinear integral equations
47H10 Fixed-point theorems
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