Convergence Theorems for Pseudomonotone Equilibrium Problem, Split Feasibility Problem, and Multivalued Strictly Pseudocontractive Mappings

“…and a weak convergence theorem for (21) with some imposed conditions on {𝜆 n }, {𝛿 n } has been established. Lately, the following new algorithm has been proposed by Abkar and Tavakkoli [43], for equilibrium problem and fixed points of two families of demicontractives in Hilbert space.…”

Section: Introductionmentioning

confidence: 99%

Inertial hybrid algorithm for generalized mixed equilibrium problems, zero problems, and fixed points of some nonlinear mappings in the intermediate sense

Ahmad,

Kumam,

Harbau

et al. 2024

Math Methods in App Sciences

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In this work, we establish the closedness and convexity of the set of fixed points of equally continuous and asymptotically demicontractive mapping in the intermediate sense. We proposed an inertial hybrid projection technique for determining an approximate common solution to three significant problems. The first is the system of generalized mixed equilibrium problems with relaxed monotone mappings, the second is the problem of fixed points of a countable family of equally continuous and asymptotically demicontractive mappings in the intermediate sense, and the third is of determining a point in a null space of a countable family of inverse strongly monotone mappings in Hilbert space. Based on these problems, we formulate a theorem and establish its strong convergence to their common solution. Additionally, we studied the applications of our algorithm to variational inequality problems and convex optimization problems. Finally, we numerically demonstrate the efficiency and robustness of our scheme. Several results available in the literature can be obtained as special cases of our result.

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“…Recently, Hu et al [28] introduced and studied the LP well-posedness of the SVI (5) in reflexive Banach spaces. For more details regarding SVIs, the reader is referred to [17,29,30] and references therein. Observe that if C = Q, f = g, H 1 = H 2 = H and A = I, where I denotes the identity operator, then the SVI ( 5) is reduced to the classical VI (1).…”

Section: Introductionmentioning

confidence: 99%

Levitin-Polyak Well-posedness for Split Equilibrium Problems

Dey¹,

Gibali²,

Reich³

2022

Preprint

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The notion of well-posedness has drawn the attention of many researchers in nonlinear analysis in connection with problems where the exact solution is unknown or may be costly to compute. Well-posedness guarantees the convergence of a sequence of approximate solutions obtained by iterative methods to the exact solution of the given problem. Motivated by these facts, we extend here the concept of Levitin-Polyak well-posedness to split equilibrium problems in infinite-dimensional Hilbert spaces. We establish, in particular, a metric characterization of Levitin-Polyak wellposedness by perturbations. We also show an equivalence between Levitin-Polyak well-posedness by perturbations for split equilibrium problems and the existence and uniqueness of their solutions under certain finite-dimensional assumptions on the mappings involved.

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Convergence Theorems for Pseudomonotone Equilibrium Problem, Split Feasibility Problem, and Multivalued Strictly Pseudocontractive Mappings

Cited by 6 publications

References 26 publications

Inertial hybrid S-iteration algorithm for fixed point of asymptotically nonexpansive mappings and equilibrium problems in a real Hilbert space

Inertial hybrid S-iteration algorithm for fixed point of asymptotically nonexpansive mappings and equilibrium problems in a real Hilbert space

Inertial hybrid algorithm for generalized mixed equilibrium problems, zero problems, and fixed points of some nonlinear mappings in the intermediate sense

Levitin-Polyak Well-posedness for Split Equilibrium Problems

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