A common solution of generalized equilibrium problems and fixed points of pseudo-contractive-type maps

Nnakwe, M. O.; Okeke, C. C.

doi:10.1007/s12190-020-01457-x

Cited by 5 publications

(3 citation statements)

References 35 publications

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“…The following notions will be used in what follows: Here we remark that this notion under different concepts has been studied by numerous authors; see, e.g., [21,22,23]. Currently, there is a growing interest in the study of G -fixed point and we refer to [20,24,25,26,27] for some interesting results.…”

Section: Resultsmentioning

confidence: 99%

Geometric inequalities for solving variational inequality problems in certain Banach spaces

2023

J. Nonlinear Var. Anal.

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In this paper, we develop some new geometric inequalities in p-uniformly convex and uniformly smooth real Banach spaces with p > 1. We use the inequalities as tools to obtain the strong convergence of the sequence generated by a subsgradient method to a solution that solves fixed point and variational inequality problems. Furthermore, the convergence theorem established can be applicable in, for example, L p (Ω), where Ω ⊂ R is bounded set and l p (R) for p ∈ (2, ∞). Finally, numerical implementations of the proposed method in the real Banach space L 5 ([−1, 1]) are presented.

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Section: Resultsmentioning

confidence: 99%

Geometric inequalities for solving variational inequality problems in certain Banach spaces

2023

J. Nonlinear Var. Anal.

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“…Currently, there is a growing interest in the study of J-fixed point (see, e.g. ; [14,20,40], for some interesting results concerning J-fixed point).…”

Section: Applications and Numerical Illustrationsmentioning

confidence: 99%

Relaxed modified Tseng algorithm for solving variational inclusion problems in real Banach spaces with applications

ABUBAKAR¹,

POOM²,

DUANGKAMON³

et al. 2022

CJM

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"In this paper, relaxed and relaxed inertial modified Tseng algorithms for approximating zeros of sum of two monotone operators whose zeros are fixed points or J-fixed points of some nonexpansive-type mappings are introduced and studied. Strong convergence theorems are proved in the setting of real Banach spaces that are uniformly smooth and 2-uniformly convex. Furthermore, applications of the theorems to the concept of J-fixed point, convex minimization, image restoration and signal recovery problems are also presented. In addition, some interesting numerical implementations of our proposed methods in solving image recovery and compressed sensing problems are presented. Finally, the performance of our proposed methods are compared with that of some existing methods in the literature."

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“…Nnakwe [36] in 2020, also applied this concept of J-fixed point and proved a strong converge theorem for approximating a common solution of variational inequality and two convex minimization problems. For more recent works on J-fixed points; see, for example, [14,37,48,55].…”

Section: Example 12 Letmentioning

confidence: 99%

Strong convergence theorems for variational inequalities and fixed point problems in Banach spaces

Nnakwe¹,

EZEORA²

2021

CJM

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In this paper, using a sunny generalized non-expansive retraction which is different from the metric projection and generalized metric projection in Banach spaces, we present a retractive iterative algorithm of Krasnosel’skii-type, whose sequence approximates a common solution of a mono-variational inequality of a finite family of η-strongly-pseudo-monotone-type maps and fixed points of a countable family of generalized non-expansive-type maps. Furthermore, some new results relevant to the study are also presented. Finally, the theorem proved complements, improves and extends some important related recent results in the literature.

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A common solution of generalized equilibrium problems and fixed points of pseudo-contractive-type maps

Cited by 5 publications

References 35 publications

Geometric inequalities for solving variational inequality problems in certain Banach spaces

Geometric inequalities for solving variational inequality problems in certain Banach spaces

Relaxed modified Tseng algorithm for solving variational inclusion problems in real Banach spaces with applications

Strong convergence theorems for variational inequalities and fixed point problems in Banach spaces

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