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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 73, 2024 - Issue 3
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Research Article

Hölder continuity of solution maps to parametric set-valued Ky Fan inequalities

Pages 623-640 | Received 28 Sep 2020, Accepted 26 Aug 2022, Published online: 14 Sep 2022

References

  • Alleche B. Multivalued mixed variational inequalities with locally Lipschitzian and locally cocoercive multivalued mappings. J Math Anal Appl. 2013;399(2):625–637.
  • Shih MH, Tan KK. Browder–Hartman–Stampacchia variational inequalities for multi-valued monotone operators. J Math Anal Appl. 1988;134(2):431–440.
  • Kassay G, Rădulescu VD. Equilibrium problems and applications. New York: Academic Press; 2018.
  • Bigi G, Castellani M, Pappalardo M, et al. Nonlinear programming techniques for equilibria. Cham: Springer; 2019.
  • Peng ZY, Wang XF, Yang XM. Connectedness of approximate efficient solutions for generalized semi-infinite vector optimization problems. Set-Valued Var Anal. 2019;27(1):103–118.
  • Peng ZY, Wang ZY, Yang XM. Connectedness of solution sets for weak generalized symmetric Ky Fan inequality problems via addition-invariant sets. J Optim Theory Appl. 2020;185(1):188–206.
  • Alleche B, Rădulescu VD. Further on set-valued equilibrium problems and applications to Browder variational inclusions. J Optim Theory Appl. 2017;175(1):39–58.
  • Alleche B, Rădulescu VD. Solutions and approximate solutions of quasi-equilibrium problems in Banach spaces. J Optim Theory Appl. 2016;170(2):629–649.
  • Fu JY, Wan AH. Generalized vector equilibrium problems with set-valued mappings. Math Methods Oper Res. 2002;56(2):259–268.
  • Kristály A, Varga C. Set-valued versions of Ky Fan's inequality with application to variational inclusion theory. J Math Anal Appl. 2003;282(1):8–20.
  • Li SJ, Liu HM, Chen CR. Lower semicontinuity of parametric generalized weak vector equilibrium problems. Bull Aust Math Soc. 2010;81(1):85–95.
  • Chen B, Gong XH. Continuity of the solution set to parametric set-valued weak vector equilibrium problems. Pacific J Optim. 2010;6(3):511–520.
  • Chen B, Huang NJ. Continuity of the solution mapping to parametric generalized vector equilibrium problems. J Global Optim. 2013;56(4):1515–1528.
  • Chen CR, Li SJ, Teo KL. Solution semicontinuity of parametric generalized vector equilibrium problems. J Global Optim. 2009;45(2):309–318.
  • Han Y, Gong XH. Semicontinuity of solution mappings to parametric generalized vector equilibrium problems. Numer Funct Anal Optim. 2016;37(11):1420–1437.
  • Peng ZY, Zhao Y, Yang XM. Semicontinuity of approximate solution mappings to parametric set-valued weak vector equilibrium problems. Numer Funct Anal Optim. 2015;36(4):481–500.
  • Anh LQ, Duoc PT, Tam TN. On the stability of approximate solutions to set-valued equilibrium problems. Optimization. 2020;69(7–8):1583–1599.
  • Peng ZY, Yang XM, Peng JW. On the lower semicontinuity of the solution mappings to parametric weak generalized Ky Fan inequality. J Optim Theory Appl. 2012;152(1):256–264.
  • Peng ZY, Peng JW, Long XJ, et al. On the stability of solutions for semi-infinite vector optimization problems. J Global Optim. 2018;70(1):55–69.
  • Anh LQ, Khanh PQ. On the Hölder continuity of solutions to parametric multivalued vector equilibrium problems. J Math Anal Appl. 2006;321(1):308–315.
  • Anh LQ, Khanh PQ. Uniqueness and Hölder continuity of the solution to multivalued equilibrium problems in metric spaces. J Global Optim. 2007;37(3):449–465.
  • Anh LQ, Khanh PQ. Sensitivity analysis for multivalued quasiequilibrium problems in metric spaces: Hölder continuity of solutions. J Global Optim. 2008;42(4):515–531.
  • Li SJ, Li XB, Wang LN, et al. The Hölder continuity of solutions to generalized vector equilibrium problems. Eur J Oper Res. 2009;199(2):334–338.
  • Li SJ, Li XB. Hölder continuity of solutions to parametric weak generalized Ky Fan inequality. J Optim Theory Appl. 2011;149(3):540–553.
  • Sadeqi I, Salehi Paydar M. Lipschitz continuity of an approximate solution mapping for parametric set-valued vector equilibrium problems. Optimization. 2016;65(5):1003–1021.
  • Han Y. Lipschitz continuity of approximate solution mappings to parametric generalized vector equilibrium problems. J Optim Theory Appl. 2018;178(3):763–793.
  • Peng ZY, Yang XM, Teo KL. On the Hölder continuity of approximate solution mappings to parametric weak generalized Ky Fan inequality. J Ind Manag Optim. 2015;11(2):549–562.
  • Han Y. Nonlinear scalarizing functions in set optimization problems. Optimization. 2019;68(9):1685–1718.
  • Anh LQ, Khanh PQ, Tam TN. On Hölder continuity of solution maps of parametric primal and dual Ky Fan inequalities. TOP. 2015;23(1):151–167.
  • Li XB, Long XJ, Zeng J. Hölder continuity of the solution set of the Ky Fan inequality. J Optim Theory Appl. 2013;158(2):397–409.
  • Kuczma M. An introduction to the theory of functional equations and inequalities: Cauchy's equation and Jensen's inequality. Berlin: Springer Science & Business Media; 2009.
  • Fan K. Some properties of convex sets related to fixed point theorems. Math Ann. 1984;266(4):519–537.
  • Singh SP, Watson B, Srivastava P. Fixed point theory and best approximation: the KKM-map principle. Vol. 424, Dordrecht: Springer Science & Business Media; 2013.
  • Kassay G, Miholca M. Vector quasi-equilibrium problems for the sum of two multivalued mappings. J Optim Theory Appl. 2016;169(2):424–442.

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