集值均衡与Browder变分包含问题解的存在性
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摘要
本文利用Ky Fan引理,研究在锥情形下集值均衡问题解的存在性,推广了近期文献中的相关结果,并在锥形式下,讨论Browder变分包含问题.
In this paper, we deal with the existence of the solution of set-valued equilibrium problems in the cone by using Ky Fan lemma. Moreover, we study Browder variational inclusion problem in the case of cone and extend the related results in the recent literature.
In this paper, we deal with the existence of the solution of set-valued equilibrium problems in the cone by using Ky Fan lemma. Moreover, we study Browder variational inclusion problem in the case of cone and extend the related results in the recent literature.
引文
[1]ALLECHE B.On hemicontinuity of bifunctions for solving equilibrium problems[J].Adv.Nonlinear Anal.,2014,3(2):69-80.
[2]ALLECHE B.Semicontinuity of bifunctions and applications to regularization methods for equilibrium problems[J/OL]Afr.Mat.,2014.http://dx.doi.org/10.1007/s13370-014-0308-1.
[3]ALLECHE B,RADULESCU V D.Equilibrium problem techniques in the qualitative analysis of quasi-hemivariational inequalities[J].Optimization,2015,64(9):1855-1868.
[4]LASZLO S,VIOREL A.Densely defined dquilibrium problems[J].J.Optim.Theory Appl.,2015,166(1):52-75.
[5]KRISTALY A,VARGA C.Set-valued versions of Ky Fan’s inequality with application to variational inclusion theory[J].J.Math.Anal.Appl.,2003,282:8-20.
[6]CASTELLANI M,GIULI M.Ekeland’s principle for cyclically antimonotone equilibrium problems[J].Nonlinear Analysis:Real World Applications.,2016,32:213-228.
[7]ALLECHE B,RADULESCU V D.Set-valued equilibrium problems with applications to Browder variational inclusions and to fixed point theory[J].Nonlinear Analysis:Real World Applications.,2016,28:251-268.
[8]FAN K.A generalization of Tychonoff’s fixed point theorem[J].Math.Ann.,1961,142(3):305-310.
[9]ALLECHE B.Multivalued mixed variational inequalities with locally Lipschitzian and locally cocoercive multivalued mappings[J].J.Math.Anal.Appl.,2013,399(2):625-637.
[10]DUREA M.Variational inclusions for contingent derivative of set-valued maps[J].J.Math.Anal.Appl.,2004,292(2):351-363.
[11]LASZLO S.Multivalued variational inequalities and coincidence point results[J].J.Math.Anal.Appl.,2013,404(1):105-114.
[2]ALLECHE B.Semicontinuity of bifunctions and applications to regularization methods for equilibrium problems[J/OL]Afr.Mat.,2014.http://dx.doi.org/10.1007/s13370-014-0308-1.
[3]ALLECHE B,RADULESCU V D.Equilibrium problem techniques in the qualitative analysis of quasi-hemivariational inequalities[J].Optimization,2015,64(9):1855-1868.
[4]LASZLO S,VIOREL A.Densely defined dquilibrium problems[J].J.Optim.Theory Appl.,2015,166(1):52-75.
[5]KRISTALY A,VARGA C.Set-valued versions of Ky Fan’s inequality with application to variational inclusion theory[J].J.Math.Anal.Appl.,2003,282:8-20.
[6]CASTELLANI M,GIULI M.Ekeland’s principle for cyclically antimonotone equilibrium problems[J].Nonlinear Analysis:Real World Applications.,2016,32:213-228.
[7]ALLECHE B,RADULESCU V D.Set-valued equilibrium problems with applications to Browder variational inclusions and to fixed point theory[J].Nonlinear Analysis:Real World Applications.,2016,28:251-268.
[8]FAN K.A generalization of Tychonoff’s fixed point theorem[J].Math.Ann.,1961,142(3):305-310.
[9]ALLECHE B.Multivalued mixed variational inequalities with locally Lipschitzian and locally cocoercive multivalued mappings[J].J.Math.Anal.Appl.,2013,399(2):625-637.
[10]DUREA M.Variational inclusions for contingent derivative of set-valued maps[J].J.Math.Anal.Appl.,2004,292(2):351-363.
[11]LASZLO S.Multivalued variational inequalities and coincidence point results[J].J.Math.Anal.Appl.,2013,404(1):105-114.