Mareşan, Viorica Volterra integral equations with iterations of linear modification of the argument. (English) Zbl 1091.45002 Novi Sad J. Math. 33, No. 2, 1-10 (2003). Let \(A(x)(t)\) denote the operator \(A(x)(t)=x(0)+\int_0^t f(s,x(s),x(\lambda s),x(\lambda x(\lambda s)))\,ds\), \(t\in[0,b]\), \(0<\lambda<1\). The author considers the integral equation \(x(t)=A(x)(t)\), where \(f\in C([0,b]^4)\). Supposing some properties related to the operator \(A\), he proves the existence, uniqueness and dependence of the solutions to equation \(x(t)=A(x)(t)\), \(t\in[0,b]\), \(0<\lambda<1\), on the data in it. These results are in a sense generalizations of those already published. Reviewer: Bogoljub Stanković (Novi Sad) Cited in 2 Documents MSC: 45G10 Other nonlinear integral equations Keywords:weakly Picard operators; modified arguments; fixed points; nonlinear Volterra integral equation PDFBibTeX XMLCite \textit{V. Mareşan}, Novi Sad J. Math. 33, No. 2, 1--10 (2003; Zbl 1091.45002) Full Text: EuDML EMIS