Abstract

The iterations scheme generated by an infinite sequence of operators satisfying some contractive conditions in a complete metric space is used to solve some integral equations of Hammerstein type.

Highlights

  • Iterations processes are powerful tools for solving both differential and integral equations in a complete metric space

  • First we prove by mathematical induction on n ∈ N0, with N0 = N \ {0} that for all u, v ∈ L1(Ω) and all n, m ∈ N0 we have

  • Assume that (2.15) is true for n = r, we prove it for n = r + 1

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Summary

SOLVING SOME NONLINEAR EQUATIONS BY SUCCESSIVE APPROXIMATIONS

The iterations scheme generated by an infinite sequence of operators satisfying some contractive conditions in a complete metric space is used to solve some integral equations of Hammerstein type.

Introduction
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