288
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

S-iterative algorithm for solving variational inequalities

, &
Pages 435-448 | Received 20 Dec 2018, Accepted 05 Apr 2020, Published online: 04 May 2020

References

  • R.P. Agarwal, D. O'Regan, D.R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings. J. Nonlinear Convex Anal. 8 (2007), pp. 61–79.
  • Q.H. Ansari, E. Köbis, and J.-C. Yao, Vector Variational Inequalities and Vector Optimization: Theory and Applications, Springer, Berlin, 2018.
  • M. Aslam Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl.251 (2000), pp. 217–229. doi: 10.1006/jmaa.2000.7042
  • V. Berinde, On a family of first order difference inequalities used in the iterative approximation of fixed points, Creat. Math. Inform. 18 (2009), pp. 110–122.
  • P. Cholamjiak and S. Suantai, Iterative methods for solving equilibrium problems, variational inequalities and fixed points of nonexpansive semigroups, J. Glob. Optim. 57 (2013), pp. 1277–1297. doi: 10.1007/s10898-012-0029-7
  • S.C. Dafermos and S.C. McKelvey, Partitionable variational inequalities with applications to network and economic equilibria, J. Optim. Theory Appl. 73 (1992), pp. 243–268. doi: 10.1007/BF00940180
  • F. Gürsoy, M. Ertürk, M. Abbas, A Picard-type iterative algorithm for general variational inequalities and nonexpansive mappings, Numer. Algor. 83 (2020), pp. 867–883.
  • F. Giannessi, ed., Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, Vol. 38, Kluwer Academic Publishers, Dordrecht, 2000.
  • S. Ishikawa, Fixed point by a new iteration method, Proc. Amer. Math. Soc. 44 (1974), pp. 147–150. doi: 10.1090/S0002-9939-1974-0336469-5
  • D. Kinderlehrar and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, 1980.
  • K. Knopp, Infinite Sequences and Series, Dover Publications, Inc., New York, 1956.
  • W.R. Mann, Mean value methods in iterations, Proc. Amer. Math. Soc. 4 (1953), pp. 506–510. doi: 10.1090/S0002-9939-1953-0054846-3
  • M.A. Noor and Z. Huang, Three-step methods for nonexpansive mappings and variational inequalities, Appl. Math. Comput. 187 (2007), pp. 680–685.
  • E. Picard, Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives, J. Math. Pures Appl. 6 (1890), pp. 145–210.
  • Y. Shehu and P. Cholamjiak, Iterative method with inertial for variational inequalities in Hilbert spaces, Calcolo (2019). Available at https://doi.org/10.1007/s10092-018-0300-5.
  • G. Stampacchia, Formes bilinearies coercivities sur les ensembles convexes, C. R. Acad. Sci. Paris 258 (1964), pp. 4413–4416.
  • R. Suparatulatorn, W. Cholamjiak, and S. Suantai, A modified S-iteration process for G-nonexpansive mappings in Banach spaces with graphs, Numer. Algor. 77 (2018), pp. 479–490. doi: 10.1007/s11075-017-0324-y
  • R.U. Verma, Generalized system for relaxed cocoercive variational inequalities and projection methods, J. Optim. Theory Appl. 121 (2004), pp. 203–210. doi: 10.1023/B:JOTA.0000026271.19947.05
  • X. Weng, Fixed point iteration for local strictly pseudocontractive mapping, Proc. Amer. Math. Soc.113 (1991), pp. 727–731. doi: 10.1090/S0002-9939-1991-1086345-8

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.