A new iterative algorithm for a generalized mixed equilibrium problem and a countable family of nonexpansive-type maps with applications

Chidume, C. E.; Nnakwe, M. O.; Otubo, E

doi:10.24193/fpt-ro.2020.1.08

Cited by 9 publications

(9 citation statements)

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“…Consequently, approximating solutions of (4.2) is equivalent to approximating J-fixed points of maps T : X → 2 X * defined by T := J -A. This connection is now generating considerable research interest in the study of J-fixed points (see, e.g., Chidume and Idu [11], Chidume and Monday [13], Chidume et al [15,16], and the references contained in them). This notion turns out to be very useful and applicable in approximating solutions of Eq.…”

Section: Application To J-fixed Pointmentioning

confidence: 99%

A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications

Chidume

Adamu

2020

Fixed Point Theory Appl

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An inertial iterative algorithm for approximating a point in the set of zeros of a maximal monotone operator which is also a common fixed point of a countable family of relatively nonexpansive operators is studied. Strong convergence theorem is proved in a uniformly convex and uniformly smooth real Banach space. This theorem extends, generalizes and complements several recent important results. Furthermore, the theorem is applied to convex optimization problems and to J-fixed point problems. Finally, some numerical examples are presented to show the effect of the inertial term in the convergence of the sequence of the algorithm.

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Section: Application To J-fixed Pointmentioning

confidence: 99%

A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications

Chidume

Adamu

2020

Fixed Point Theory Appl

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“…Let X be a smooth real Banach space with dual space X * . The map ψ : [23], and a host of other authors. It is easy to see from the definition of the map ψ that…”

Section: Preliminariesmentioning

confidence: 99%

A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications

Chidume

Nnakwe

Adamu

2019

Fixed Point Theory Appl

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Let X be a uniformly convex and uniformly smooth real Banach space with dual space X *. In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-strongly monotone map is constructed. A strong convergence theorem for a sequence generated by the algorithm is proved. Furthermore, the theorem is applied to approximate the solution of a convex optimization problem, a Hammerstein integral equation, and a variational inequality problem. This theorem generalizes, improves, and complements some recent results. Finally, examples of generalized-Φ-strongly monotone maps are constructed and numerical experiments which illustrate the convergence of the sequence generated by our algorithm are presented.

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“…Thus, the inverse of J may not exist. For more recent works on J-fixed points, see, for example, [40][41][42][43][44][45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

An algorithm for approximating a common solution of some nonlinear problems in Banach spaces with an application

Bello

Nnakwe

2021

Adv Differ Equ

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In this paper, we construct a new Halpern-type subgradient extragradient iterative algorithm. The sequence generated by this algorithm converges strongly to a common solution of a variational inequality, an equilibrium problem, and a J-fixed point of a continuous J-pseudo-contractive map in a uniformly smooth and two-uniformly convex real Banach space. Also, the theorem is applied to approximate a common solution of a variational inequality, an equilibrium problem, and a convex minimization problem. Moreover, a numerical example is given to illustrate the implementability of our algorithm. Finally, the theorem proved complements, improves, and unifies some related recent results in the literature.

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A new iterative algorithm for a generalized mixed equilibrium problem and a countable family of nonexpansive-type maps with applications

Cited by 9 publications

References 0 publications

A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications

A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications

A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications

An algorithm for approximating a common solution of some nonlinear problems in Banach spaces with an application

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