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Existence and iterative approximation of solutions of generalized mixed quasi-variational-like inequality problem in Banach spaces. (English) Zbl 1227.65059
This paper is concerned with an approximation of solutions to a generalized mixed quasivariational inequality problem in the setting of Banach spaces. By using the auxiliary technique, the authors propose an iterative process to approximate the solution of the problem. They prove that the iterative sequence generated converges to the unique solution of the problem.

65K15Numerical methods for variational inequalities and related problems
49J40Variational methods including variational inequalities
Full Text: DOI
[1] Antipin, A. S.: Iterative gradient prediction-type methods for computing fixed-point of extremal mappings, Parametric optimization and related topic IV, 11-24 (1997) · Zbl 0958.49022
[2] Ansari, Q. H.; Yao, J. C.: Iterative schemes for solving mixed variational-like inequalities, J. optim. Theory appl. 108, No. 3, 527-541 (2001) · Zbl 0999.49008 · doi:10.1023/A:1017531323904
[3] Chen, X. H.; Liu, Y. F.: On the generalized nonlinear variational-like inequalities in reflexive Banach space, J. Nanjing univ. Math. biquart. 18, No. 1, 96-103 (2001) · Zbl 1003.47050
[4] Cubiotti, P.: Existence of solutions for lower semicontinuous quasi equilibrium problems, Comput. math. Appl. 30, 11-22 (1995) · Zbl 0844.90094 · doi:10.1016/0898-1221(95)00171-T
[5] Ding, X. P.: General algorithm for nonlinear variational-like inequalities in reflexive Banach spaces, Indian J. Pure appl. Math. 29, No. 2, 109-120 (1998) · Zbl 0908.49009
[6] Ding, X. P.: Existence and algorithm of solutions for nonlinear mixed variational-like inequalities in Banach spaces, J. comput. Appl. math. 157, 419-434 (2003) · Zbl 1040.65053 · doi:10.1016/S0377-0427(03)00421-7
[7] Ding, X. P.: Predictorcorrector iterative algorithms for solving generalized mixed variational-like inequalities, Appl. math. Comput. 152, No. 3, 855-865 (2004) · Zbl 1077.49004 · doi:10.1016/S0096-3003(03)00602-7
[8] Fang, Y. P.; Huang, N. J.: Variational-like inequalities with generalized monotone mappings in Banach spaces, J. optim. Theory appl. 118, No. 2, 327-338 (2003) · Zbl 1041.49006 · doi:10.1023/A:1025499305742
[9] Hartman, P.; Stampacchia, G.: On some nonlinear elliptic differential functional equations, Acta. math. 115, 271-310 (1966) · Zbl 0142.38102 · doi:10.1007/BF02392210
[10] Hanson, M. A.: On sufficiency of the Kuhn -- Tucker conditions, J. math. Anal. appl. 80, 545-550 (1981) · Zbl 0463.90080 · doi:10.1016/0022-247X(81)90123-2
[11] Huang, N. J.; Deng, C. X.: Auxiliary principle and iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities, J. math. Anal. appl. 256, 345-359 (2001) · Zbl 0972.49008 · doi:10.1006/jmaa.2000.6988
[12] Huang, N. J.; Fang, Y. P.; Cho, Y. J.: A new class of generalized nonlinear mixed quasi-variational inequalities in Banach space, Math. ineq.& appl. 6, No. 1, 125-132 (2003) · Zbl 1032.47042
[13] Liu, Z.; Chen, Z.; Kang, S. M.; Ume, J. S.: Existence and iterative approximations of solutions for mixed quasi-variational-like inequalities in Banach spaces, Nonlinear anal. 69, 3259-3272 (2008) · Zbl 1182.47048 · doi:10.1016/j.na.2007.09.015
[14] Noor, M. A.; Memon, Z. A.: Algorithms for general mixed quasi variational inequalities, J. inequal. Pure appl. Math. 3, No. 4, 59 (2002) · Zbl 1022.49003 · http://jipam-old.vu.edu.au/v3n4/
[15] Pascali, D.; Sburlan, S.: Nonlinear mappings of monotone type, (1978) · Zbl 0423.47021
[16] Panagiotopoulos, P. D.; Stavroulakis, G. E.: New types of variational principles based on the notion of quasi differentiability, Acta mech. 94, 171-194 (1992) · Zbl 0756.73096 · doi:10.1007/BF01176649
[17] Rus, I. A.: Generalized contractions and applications, (2001) · Zbl 0968.54029
[18] Tian, G.: Generalized quasi variational-like inequality problem, Math. oper. Res. 18, 752-764 (1993) · Zbl 0811.49010 · doi:10.1287/moor.18.3.752
[19] Verma, R. U.: A new class of iterative algorithms for approximation-solvability of nonlinear variational inequalities, Comput. math. Appl. 41, No. 3-4, 505512 (2001) · Zbl 0980.49012 · doi:10.1016/S0898-1221(00)00292-3
[20] R.U. Verma, Generalized partially relaxed pseudomonotone variational inequalities and general auxiliary problem principle, J. Ineq. Appl., Article ID 90295, 2006, p. 12, doi:doi:10.1155/JIA/2006/90295. · Zbl 1090.49017 · doi:10.1155/JIA/2006/90295
[21] Zeng, L. C.: On a general projection algorithm for variational inequalities, J. optim. Theory appl. 97, No. 1, 229-235 (1998) · Zbl 0907.90265 · doi:10.1023/A:1022687403403
[22] Zeng, L. C.: Iterative approximation of solutions to generalized set-valued strongly nonlinear mixed variational-like inequalities, Acta math. Sin. 48, No. 5, 879-888 (2005) · Zbl 1124.49306
[23] Zeng, L. C.; Ansari, Q. H.; Yao, J. C.: General iterative algorithms for solving mixed quasi-variational-like inclusions, Comput. math. Appl. 56, 2455-2467 (2008) · Zbl 1165.65355 · doi:10.1016/j.camwa.2008.05.016