Approximation of Solutions of Nonlinear Integral Equations of Hammerstein Type with Lipschitz and Bounded Nonlinear Operators

Djitte, N.; Sène, Moustapha

doi:10.5402/2012/963802

Cited by 9 publications

(3 citation statements)

References 19 publications

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“…Iterative methods for approximating solutions of problem (4.3) have been studied (see e.g., [10,12,13,15,19,22,23,26,35,42] and the references therein).…”

Section: Applications To Hammerstein Integral Equationsmentioning

confidence: 99%

Strong convergence of an inertial algorithm for maximal monotone inclusions with applications

Chidume

Adamu

Nnakwe

2020

Fixed Point Theory Appl

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An inertial iterative algorithm is proposed for approximating a solution of a maximal monotone inclusion in a uniformly convex and uniformly smooth real Banach space. The sequence generated by the algorithm is proved to converge strongly to a solution of the inclusion. Moreover, the theorem proved is applied to approximate a solution of a convex optimization problem and a solution of a Hammerstein equation. Furthermore, numerical experiments are given to compare, in terms of CPU time and number of iterations, the performance of the sequence generated by our algorithm with the performance of the sequences generated by three recent inertial type algorithms for approximating zeros of maximal monotone operators. In addition, the performance of the sequence generated by our algorithm is compared with the performance of a sequence generated by another recent algorithm for approximating a solution of a Hammerstein equation. Finally, a numerical example is given to illustrate the implementability of our algorithm for approximating a solution of a convex optimization problem.

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“…Iterative methods for approximating solutions of problem (4.3) have been studied (see e.g., [10,12,13,15,19,22,23,26,35,42] and the references therein).…”

Section: Applications To Hammerstein Integral Equationsmentioning

confidence: 99%

Strong convergence of an inertial algorithm for maximal monotone inclusions with applications

Chidume

Adamu

Nnakwe

2020

Fixed Point Theory Appl

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“…Following this, Chidume and Djitte studied this explicit coupled iterative algorithms and proved several strong convergence theorems (see, Chidume and Djitte [23,24] ). For recent results using these recursion formulas or their modifications, the reader may consult any of the following references Chidume and Djitte [25][26][27], Djitte and Sene [37,38], Chidume and Ofeodu [28], Chidume and Shehu [30] and also Chapter 13 of [21]. For Hammerstein equations involving monotone mappings from E to E * , very little has been achieved.…”

Section: Introductionmentioning

confidence: 99%

Algorithms for Hammerstein inclusions in certain Banach spaces

Sène¹,

N’Diaye²,

Djitte³

2019

J. Nonlinear Sci. Appl.

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Let E be a reflexive smooth and strictly convex real Banach space. Let F : E → 2 E * and K : E * → E be bounded maximal monotone mappings such that D(F) = E and R(F) = D(K) = E * . Suppose that the Hammerstein inclusion 0 ∈ u + KFu has a solution in E. We present in this paper a new algorithm for approximating solutions of the inclusion 0 ∈ u + KFu. Then we prove strong convergence theorems. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear mappings. Furthermore, our technique of proof is of independent interest.

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“…Following this, Chidume and Djitte studied this explicit coupled iterative algorithms and proved several strong convergence theorems (see, Chidume and Djitte [17], [18] ). For recent results using these recursion formulas, the reader may consult any of the following references Chidume and Djitte [14], [15], [16], Djitte and Sene [26], [27], Chidume and Ofeodu [19], Chidume and Shehu [21] and also Chapter 13 of [13]. For Hammerstein equations involving monotone mappings from E to E * , very little has been achieved.…”

Section: Introductionmentioning

confidence: 99%

Algorithm for Hammerstein equations with monotone mappings in certain Banach spaces

Sow¹,

Diop²,

Djitte³

2016

CMI

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For q > 1 and p > 1, let E be a 2-uniformly convex and q-uniformly smooth or p- uniformly convex and 2-uniformly smooth real Banach space and F : E → E∗, K : E∗ → E be bounded and strongly monotone maps with D(K) = R(F) = E∗. We construct a coupled iterative process and prove its strong convergence to a solution of the Hammerstein equation u + KF u = 0. Futhermore, our technique of proof is of independent of interest.

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Approximation of Solutions of Nonlinear Integral Equations of Hammerstein Type with Lipschitz and Bounded Nonlinear Operators

Cited by 9 publications

References 19 publications

Strong convergence of an inertial algorithm for maximal monotone inclusions with applications

Strong convergence of an inertial algorithm for maximal monotone inclusions with applications

Algorithms for Hammerstein inclusions in certain Banach spaces

Algorithm for Hammerstein equations with monotone mappings in certain Banach spaces

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