Approximation of solutions of Hammerstein equations with bounded strongly accretive nonlinear operators

Chidume, C. E.; Djitte, N.

doi:10.1016/j.na.2008.08.016

Cited by 22 publications

(10 citation statements)

References 28 publications

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“…With this, Chidume and Zegeye [25] were able to prove strong convergence of an iterative algorithm defined in the Cartesian product space E to a solution of the Hammerstein equation (1.1). Extensions of these early results of Chidume and Zegeye [25] were obtained by several authors (see, e.g., Chidume and Zegeye [26,27], Chidume and Djitte [15][16][17], Chidume and Ofoedu [21], Chidume and Shehu [22,23], Chidume et al [12,20] Djitte and Sene [29], Ofoedu and Onyi [39], Ofoedu and Malonza [38], Shehu [43], Minjibir and Mohammed [34], and the references contained therein).…”

Section: Theorem 11 Let H Be a Separable Hilbert Space And C Be A Clmentioning

confidence: 63%

Iterative algorithms for solutions of Hammerstein equations in real Banach spaces

Chidume

Adamu

Okereke

2020

Fixed Point Theory Appl

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Let B be a uniformly convex and uniformly smooth real Banach space with dual space B *. Let F : B → B * , K : B * → B be maximal monotone mappings. An iterative algorithm is constructed and the sequence of the algorithm is proved to converge strongly to a solution of the Hammerstein equation u + KFu = 0. This theorem is a significant improvement of some important recent results which were proved in real Hilbert spaces under the assumption that F and K are maximal monotone continuous and bounded. The continuity and boundedness restrictions on K and F have been dispensed with, using our new method, even in the more general setting considered in our theorems. Finally, numerical experiments are presented to illustrate the convergence of the sequence of our algorithm.

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Section: Theorem 11 Let H Be a Separable Hilbert Space And C Be A Clmentioning

confidence: 63%

Iterative algorithms for solutions of Hammerstein equations in real Banach spaces

Chidume

Adamu

Okereke

2020

Fixed Point Theory Appl

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“…The recursion formulas (*) and (**) have been used successfully to approximate solutions of Hammerstein equations involving nonlinear accretive-type operators. 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].…”

Section: Introductionmentioning

confidence: 93%

“…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: 93%

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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“…The recursion formulas (*) and (**) have been used successfully to approximate solutions of Hammerstein equations involving nonlinear accretive-type operators. 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].…”

Section: Introductionmentioning

confidence: 94%

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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Approximation of solutions of Hammerstein equations with bounded strongly accretive nonlinear operators

Cited by 22 publications

References 28 publications

Iterative algorithms for solutions of Hammerstein equations in real Banach spaces

Iterative algorithms for solutions of Hammerstein equations in real Banach spaces

Algorithm for Hammerstein equations with monotone mappings in certain Banach spaces

Algorithms for Hammerstein inclusions in certain Banach spaces

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