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On solutions of a quadratic integral equation of Hammerstein type

✍ Scribed by J. Banaś; J. Rocha Martin; K. Sadarangani

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
211 KB
Volume
43
Category
Article
ISSN
0895-7177

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✦ Synopsis

We study the solvability of a nonlinear quadratic integral equation of Hammerstein type. Using the technique of measures of noncompactness we prove that this equation has solutions on an unbounded interval. Moreover, we also obtain an asymptotic characterization of these solutions. Several special cases of this integral equation are discussed and applications to real world problems are indicated.

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Let E be a 2-uniformly real Banach space and F , K : E → E be nonlinear-bounded accretive operators. Assume that the Hammerstein equation u + KFu = 0 has a solution. A new explicit iteration sequence is introduced and strong convergence of the sequence to a solution of the Hammerstein equation is pr

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The existence and uniqueness solution of the nonlinear integral equation of Hammerstein type with discontinuous kernel are discussed. The normality and continuity of the integral operator are proved. Toeplitz matrix method is used, as a numerical method, to obtain a nonlinear system of algebraic equ