### Abstract

Let X be a uniformly convex and uniformly smooth real Banach space with dual X*. Let F : X → X* and K : X* → X be continuous monotone operators. Suppose that the Hammerstein equation u + KFu = 0 has a solution in X. It is proved that a hybrid-type approximation sequence converges strongly to u*, where u* is a solution of the equation u + KFu = 0. In our theorems, the operator K or F need not be defined on a compact subset of X and no invertibility assumption is imposed on K. [Figure not available: see fulltext.]

Original language | English |
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Pages (from-to) | 221-232 |

Number of pages | 12 |

Journal | Arabian Journal of Mathematics |

Volume | 2 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 1 2013 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Zegeye, H., & Malonza, D. M. (2013). Hybrid approximation of solutions of integral equations of the Hammerstein type.

*Arabian Journal of Mathematics*,*2*(2), 221-232. https://doi.org/10.1007/s40065-012-0060-z