Composite Weiner Hopf Equation with Variational Inequality and Equilibrium Problem

Savita Rathee, Monika Swami


In this paper, we introduce an iteration based on compositeWeiner-Hopf equation technique to find the common solution of the set of solution of composite generalized variational inequality, set of equilibrium problem and set of fixed point of non expansive mapping in separable real Hilbert space. As the result, the strong convergence theorem of the suggested iteration has been discussed.


CompositeWeiner-Hopf equation technique; Convergence analysis; Composite Variational inequality; Monotone operators

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E. Al-Shemas, General nonconvex Wiener-Hopf equations and general nonconvex variational inequalities, Journal of Mathematical Sciences: Advances and Applications 19(1) (2013), 1 – 11, URL:[1]%20JMSAA%207100121122%20Enab%20Al-Shemas%20[1-11].pdf.

E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, Mathematics Students 63 (1994), 123 – 145, URL:

Z. Khan, S.S. Irfan, I. Ahmad and P. Shukla, Composite generalized variational inequalities with Wiener-Hopf equations, Communications in Mathematics and Applications 11(1) (2020), 85 – 93, DOI: 10.26713%2Fcma.v11i1.1254.

N. Kikuchi and J.T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, (Series: Studies in Applied and Numerical Mathematics), SIAM Publishing Co., Philadelphia (1988), URL:

A. Moudafi abd M. Théra, Proximal and dynamical approaches to equilibrium problems, Lecture Notes in Economics and Mathematical Systems 477, Springer, New York (1999), URL:

A. Moudafi, Mixed equilibrium problems sensitivity analysis and algorithmic aspect, Computers & Mathematics with Applications 44 (2002), 1099 – 1108, DOI: 10.1016/S0898-1221(02)00218-3.

M.A. Noor, Wiener-Hopf equations and variational inequalities, Journal of Optimization Theory and Applications 79(1) (1993), 197 – 206, DOI: 10.1007/BF00941894.

M.A. Noor, Some developments in general variational inequalities, Applied Mathematics and Computation 152(1) (2004), 199 – 277, DOI: 10.1016/S0096-3003(03)00558-7.

P. Shi, Equivalence of variational inequalities with Wiener-Hopf equations, Proceedings of the American Mathematical Society 111 (1991), 339 – 346, DOI: 10.1090/S0002-9939-1991-1037224-3.

G. Stampacchia, Formes bilinéaires coercitives sur les ensembles convexes, Comptes Rendus del’Academie des Sciences, Paris 258 (1964), 4413 – 4416.

R.U. Verma, Generalized variational inequalities involving multivalued relaxed monotone operators, Applied Mathematics Letters 10 (1997), 107 – 109, DOI: 10.1016/S0893-9659(97)00068-2.

Y. Wang and C. Zhang, Weiner-Hopf equation technique for solving equilibrium problems and variational inequalities and fixed points of a nonexpansive mapping, Journal of Inequalities and Applications 2014 (2014), Article number: 286, 17 pages, DOI: 10.1186/1029-242X-2014-286.

X. Weng, Fixed point iteration for local strictly pseudo-contractive mapping, Proceedings of the American Mathematical Society 113(3) (1991), 727 – 731, DOI: 10.2307/2048608.

C. Wu, Wiener-Hopf equations methods for generalized variational equations, Journal of Nonlinear Functional Analysis 3 (2013), 1 – 10, URL:



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