Strong convergence theorem for fixed points of nearly uniformly L-Lipschitzian asymptotically generalized \Phi-hemicontractive mappings

Chidume, C. E.; Bello, A. U.; Okpala, M. E.; Ndambomve, Patrice

doi:10.12988/ijma.2015.54144

Cited by 5 publications

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“…Approximating zeros of accretive maps is equivalent to approximating fixed points of pseudo-contractive maps, assuming existence of such zeros. For earlier and more recent results on the approximation of fixed points of pseudo-contractive maps, the reader may consult any of the following: [27][28][29][30][31][32][33][34][35][36].…”

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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