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Inspired by [ 4 ], we propose a novel framework to investigate variational inclusions relying on the $$\theta $$ θ -methods. First, we define the $$\theta $$ θ -resolvent and… Click to show full abstract
Inspired by [ 4 ], we propose a novel framework to investigate variational inclusions relying on the $$\theta $$ θ -methods. First, we define the $$\theta $$ θ -resolvent and the $$\theta $$ θ -Yosida operators. Then, we provide some basic properties which are relevant to investigate the asymptotic behavior of the resulting proximal-type algorithm for a class of nonmonotone operators. A special attention is given to both the minimization and the fixed-point cases and connections with numerical methods, in these settings, are presented. Some concluding remarks are also provided.
Journal Title: Bulletin of the Iranian Mathematical Society
Year Published: 2019
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