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On a system of extended general variational inclusions

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Abstract

At the present paper, a new system of extended general nonlinear variational inclusions is introduced and using the resolvent operator technique, equivalence between the aforesaid system and the fixed point problem is verified. By using this alternative equivalent formulation, the existence and uniqueness theorem for solution of the system of extended general nonlinear variational inclusions is demonstrated and two new iterative schemes for solving this system of extended general nonlinear variational inclusions are suggested and analyzed. The convergence analysis of the proposed iterative methods under some suitable conditions is studied. Some errors in a recent article by Noor et al. (J Inequal Appl 2011:10, 2011) are found and the incorrectness of the results of the cited paper is proved. Also, the results of the aforementioned paper are revised and corrected.

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Authors and Affiliations

  1. Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran

    Javad Balooee

  2. Department of Mathematics Education and RINS, Gyeongsang National University, Chinju, 660-701, Korea

    Yeol Je Cho

Authors
  1. Javad Balooee
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  2. Yeol Je Cho
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Correspondence to Yeol Je Cho.

Additional information

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant Number: 2011-0021821).

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Balooee, J., Cho, Y.J. On a system of extended general variational inclusions. Optim Lett 7, 1281–1301 (2013). https://doi.org/10.1007/s11590-012-0503-7

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