Modified forward-backward splitting method for split equilibrium, variational inclusion, and fixed point problems
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Bibliographic record
Abstract
In the recent time, the problem of finding common solutions of fixed point problems (FPPs) of nonlinear mappings and optimization problems (OPs) has received great research attention due to its potential applications to mathematical models whose constraints can be expressed as the FPPs and OPs.In this paper, we study the problem of finding a common solution of a split equilibrium problem (SEP), a variational inclusion problem (VIP) and the FPP with a finite family of multivalued demicontractive mappings.We propose a new inertial iterative method, which employs the forward-backward splitting technique together with the viscosity method for approximating the solution of the problem in Hilbert spaces.The proposed method uses variable step sizes, which do not depend on the norm of the bounded linear operator.We prove strong convergence results under some mild conditions.Finally, we present some numerical experiments to demonstrate the efficiency and applicability of the proposed method.Our result improves and extends several existing results in the current literature in this direction.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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