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g-η-Monotone mapping and resolvent operator technique for solving generalized implicit variational-like inclusions

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Abstract

A new class of g-η-monotone mappings and a class of generalized implicit variational-like inclusions involving g-η-monotone mappings are introduced. The resolvent operator of g-η-monotone mappings is defined and its Lipschitz continuity is presented. An iterative algorithm for approximating the solutions of generalized implicit variational-like inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved.

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Author information

Correspondence to Qing-bang Zhang Doctor 张清邦.

Additional information

Contributed by DING Xie-ping

Project supported by the Key Science Foundation of Sichuan Education Department of China (No.2003A081)

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Zhang, Q., Ding, X. g-η-Monotone mapping and resolvent operator technique for solving generalized implicit variational-like inclusions. Appl Math Mech 28, 11–18 (2007) doi:10.1007/s10483-007-0102-y

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Key words

  • g-η-monotone mapping
  • resolvent operator
  • generalized implicit variational-like inclusion
  • iterative algorithm

Chinese Library Classification

  • O177.91

2000 Mathematics Subject Classification

  • 47J20
  • 49J40