Algorithm for finite family of variational inequality with fixed point of two non-expansive mappings

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Monika Swami
Savita Rathee


In the recent work, a new hybrid technique for computing the common solution of fixed point of a finite family of two non-expansive mapping and variational inequality problem for inverse strongly monotone mapping in a real Hilbert space is provided. We also demonstrate the convergence of the hybrid approach using an example.

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How to Cite
Swami, M., & Rathee, S. (2022). Algorithm for finite family of variational inequality with fixed point of two non-expansive mappings. Tamkang Journal of Mathematics, 54(3), 203–219.


C. E. Lemke and J. T. Howson, Equilibrium points of bimatrix games, J. Soc. Indust. Appl. Math., 12(1964), 413–423.

G. Marino and H. K. Xu, A general iterative method for non-expansive mappings in Hilbert spaces, Journal of Mathematical Analysis and Applications, 318(1)(2006), 43-52.

G. L. Acedo and H. K. Xu, Iterative methods for strict pseudocontractions in Hilbert spaces, Nonlinear Analysis: Theory, Methods $&$ Applications, textbf{67}(7)(2007), 2258-2271.

G. M. Korpelevich, An extragradient method for finding saddle points and for other problem, Ekonomika I Matematicheskie Metody, textbf{12}(4)(1976), 747-756.

H. E. Scarf, The approximation of fixed points of a continuous mapping, SIAM J. Appl. Math., textbf{15}(1967), 1328–1342.

H. K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc. , textbf{66}(2002), 240-256.

J. L. Lions, Quelques Methodes de Resolution des Problemes aux limites Non Lineaires, Dunod, Paris, France. textbf{1969}

K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, textbf{28}(1990), Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK.

L. Liu, S. Y. Cho and J.C. Yao, Convergence analysis of an inertial Tseng’s extragradient algorithm for solving pseudomonotone variational inequalities and applications, J. Nonlinear Var. Anal., textbf{5}(2021), 627-644.

M. Khan, M. Zeeshan and S. Iqbal, Neutrosophic variational inequalities with applications in decision-making, Soft Comput., textbf{26}(2022), 4641–4652.

O. K. Oyewole and S. Reich, A totally relaxed self-adaptive algorithm for solving a variational inequality and fixed point problems in Banach spaces, Appl. Set-Valued Anal. Optim., textbf{4}(2022), 349-366.

Q. Cheng, Hybrid viscosity approximation methods with generalized contractions for zeros of monotone operators and fixed point problems, J. Nonlinear Funct. Anal., textbf{2022}(2022), 23.

R. T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Transaction of the American Mathematical Soceity, textbf{149}(1970), 75-88.

S. Husain and N. Singh, An iterative method for finding common solution of the fixed point problem of a finite family of nonexapnsive mappings and a finite family of variational inequality problems in Hilbert Space,

Journal of Applied Mathematics, textbf{2019}(2019), 11 pages.

S. Treant$breve{a}$, Well posedness of new optimization problems with variational inequality constraints, Fractal and Fractional, textbf{5}(3)(2021), 123.

W. Takahashi and M. Toyoda, Strong convergence theorems for nonexapnsive mappings and monotone mappings, Journal of Optimization Theory and Applications, textbf{118}(2)(2003), 417-428.

Y. Yao, Y. C. Liou and J. C. Yao, Split common fixed point problem for two quasi-pseudocontractive operators and its algorithm construction, Fixed Point Theory Appl., textbf{2015}(127)(2015), 19 pages.

Y. J. Cho and X. Qin, Convergence of a general iterative method for nonexapnsive mappings in Hilbert spaces, Journal of Computational and Applied Mathematics, textbf{228}(1)(2009), 458-465.