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Existence and iterative approximations of solutions for strongly nonlinear variational-like inequalities

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In this paper, we introduce and study a new class of strongly nonlinear variational-like inequalities. Under suitable conditions, we prove the existence of solutions for the class of strongly nonlinear variational-like inequalities. By making use of the auxiliary principle technique, we suggest an iterative algorithm for the strongly nonlinear variational-like inequality and give the convergence criteria of the sequences generated by the iterative algorithm.

Abstract

In this paper, we introduce and study a new class of strongly nonlinear variational-like inequalities. Under suitable conditions, we prove the existence of solutions for the class of strongly nonlinear variational-like inequalities. By making use of the auxiliary principle technique, we suggest an iterative algorithm for the strongly nonlinear variational-like inequality and give the convergence criteria of the sequences generated by the iterative algorithm.

참고문헌 (13)

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  4. X. P. Ding, "Algorithm of solutions for mixed nonlinear variational-like inequalities in reflexive Banach space", Appl. Math. Mech. (English Ed.), 19(6), pp.521~529 (1998)
  5. X. P. Ding, "Existence and algorithm of solutions for nonlinear mixed variational-like in-equalities in Banach spaces", J. Comput. Appl. Math, 157(2), pp.419~434 (2003)
  6. X. P. Ding, "A minimax inequality with applications to existence of equilibrium point and fixed point theorems", Colloq. Math, 63(2), pp.233~247 (1992)
  7. R. Glowinski, "Numerical Analysis of Variational In-equalities" (1981), North-Holland
  8. N. J. Huang, "Auxiliary principle and iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities", J. Math. Anal. Appl, 256(2), pp.345~359 (2001)
  9. P. D. Panagiotopoulos, "New types if variational principles based on the notion of quasidifferentiability", Acta Mech, 94(3), pp.171~194 (1992)
  10. J. Parida, "A variational-like inequality for multifunctions with applications", J. Math. Anal. Appl, 124(1), pp.73~81 (1987)
  11. G. Tian, "Generalized quasi-variational-like inequality problem", Math. Oper. Res, 18(3), pp.752~764 (1993)
  12. J. C. Yao, "The generalized quasi-variational inequality problem with applications", J. Math. Anal. Appl, 158(1), pp.139~160 (1991)
  13. J. C. Yao, "Existence of generalized variational inequalities", Oper. Res. Lett, 15(1), pp.35~40 (1994)

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