Forward-reflected-backward splitting method without cocoercivity for the sum of maximal monotone operators in Banach spaces

Bello, A. U.; Okeke, C. C.; Isyaku, M.; Omojola, M. T.

doi:10.1080/02331934.2022.2057308

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2022

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“…Extension of the VIP (1.1) to Banach spaces more general than Hilbert spaces is currently of interest to many authors (see, e.g. ; [44], [12], [4], [28] and the references there in). In 2019, Shehu [46] extended the Theorem of Tseng [50] to real Banach spaces.…”

Section: Introductionmentioning

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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