136
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Viscosity approximation method for split best proximity point and monotone variational inclusion problem

&

References

  • M. Abdellatif, Split monotone variational inclusions, J. Optim. Theory Appl. 150 (2011), pp. 275–283.
  • R.P. Agarwal, D. O'Regan, and D. Sahu, Fixed Point Theory for Lipschitzian-type Mappings with Applications Vol. 6, Springer, 2009.
  • T.O. Alakoya, A. Taiwo, O.T. Mewomo, and Y.J. Cho, An iterative algorithm for solving variational inequality, generalized mixed equilibrium, convex minimization and zeros problems for a class of nonexpansive-type mappings, Ann. Univ. Ferrara 67 (2021), pp. 1–31.
  • Q.H. Ansari and A. Rehan, An iterative method for split hierarchical monotone variational inclusions, Fixed Point Theory Appl. 2015 (2015), pp. 1–10.
  • S.S. Basha, Best proximity points: optimal solutions, J. Optim. Theory Appl. 151 (2011), pp. 210–216.
  • H.H. Bauschke and J.M. Borwein, On projection algorithms for solving convex feasibility problems, SIAM Rev. 38 (1996), pp. 367–426.
  • N. Bunlue and S. Suantai, Hybrid algorithm for common best proximity points of some generalized nonself nonexpansive mappings, Math. Methods Appl. Sci. 41 (2018), pp. 7655–7666.
  • C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Probl.18 (2002), p. 441–453.
  • Y. Censor, T. Bortfeld, B. Martin, and A. Trofimov, A unified approach for inversion problems in intensity-modulated radiation therapy, Phys. Med. Biol. 51 (2006), pp. 2353–2365.
  • Y. Censor, A. Gibali, and S. Reich, Algorithms for the split variational inequality problem, Numer. Algorithms 59 (2012), pp. 301–323.
  • P. Combettes, The convex feasibility problem in image recovery, in Advances in Imaging and Electron Physics, Vol. 95, Elsevier, 1996, pp. 155–270.
  • G. Crombez, A hierarchical presentation of operators with fixed points on Hilbert spaces, Numer. Funct. Anal. Optim. 27 (2006), pp. 259–277.
  • J. Deepho, J. Martínez Moreno, K. Sitthithakerngkiet, and P. Kumam, Convergence analysis of hybrid projection with Cesàro mean method for the split equilibrium and general system of finite variational inequalities, J. Comput. Appl. Math. 318 (2017), pp. 658–673.
  • J. Eckstein and B.F. Svaiter, A family of projective splitting methods for the sum of two maximal monotone operators, Math. Program. 111 (2008), pp. 173–199.
  • M. Gabeleh, Best proximity point theorems via proximal non-self mappings, J. Optim. Theory Appl. 164 (2015), pp. 565–576.
  • E. Godwin, C. Izuchukwu, and O. Mewomo, An inertial extrapolation method for solving generalized split feasibility problems in real Hilbert spaces, Bolletino Unione Mat. Italian 14 (2021), pp. 379–401.
  • K. Goebel and W.A. Kirk, Topics in Metric Fixed Point Theory Vol. 28, Cambridge university press, 1990.
  • S.P. Han and G. Lou, A parallel algorithm for a class of convex programs, SIAM J. Control Optim. 26 (1988), pp. 345–355.
  • P.L. Lions and B. Mercier, Splitting algorithms for the sum of two nonlinear operators, SIAM J. Numer. Anal. 16 (1979), pp. 964–979.
  • A. Moudafi, Viscosity approximation methods for fixed-points problems, J. Math. Anal. Appl. 241 (2000), pp. 46–55.
  • G.B. Passty, Ergodic convergence to a zero of the sum of monotone operators in Hilbert space, J. Math. Anal. Appl. 72 (1979), pp. 383–390.
  • V.S. Raj, Best proximity point theorems for non-self mappings, Fixed Point Theory 14 (2013), pp. 447–454.
  • B.S Sadiq, Best proximity points: global optimal approximate solutions, J. Glob. Optim. 49 (2011), pp. 15–21.
  • S. Saejung and P. Yotkaew, Approximation of zeros of inverse strongly monotone operators in Banach spaces, Nonlinear Anal. Theory Methods Appl. 75 (2012), pp. 742–750.
  • S. Suantai and J. Tiammee, The shrinking projection method for solving split best proximity point and equilibrium problems, Filomat 35 (2021), pp. 1133–1140.
  • R. Suparatulatorn and S. Suantai, A new hybrid algorithm for global minimization of best proximity points in Hilbert spaces, Carpathian J. Math. 35 (2019), pp. 95–102.
  • J. Tiammee and S. Suantai, On solving split best proximity point and equilibrium problems in Hilbert spaces, Carpathian J. Math. 35 (2019), pp. 385–392.

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.