References
- D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications, Academic Press, 1980.
- J. P. Aubin, Mathematical methods of game theory and economics, North Holland, Amsterdam, The Netherlands, 1982.
- H. Brezis, Operateurs maximaux monotone er semi groupes de contractions dans les espaces de Hilbert, North-Holland Mathematices Studies 5 Notes de Matematica (50) North-Holland, Amsterdam, 1973.
- R. E. Bruck and S. Reich, Accretive operators, Banach limits and dual ergodic theorems, Bull. Acad. Polon Sci. 12 (1981), 585-589
- R. Glowinski, J. L. Lions and R. Tremolieres, Numerical analysis of variational inequalities, North-Holland, Amsterdam, 1981.
- F. Giannessi and A. Mugeri, Variational inequalities and network equilibrium problems, Plenum Press, New York NY USA, 1995.
- L. Gioranescu, Geometry of Banach spaces, duality mapping and nonlinear problems, kluwer Acad. Press, Amsterdam, 1990.
- N. Kikuchi and J. T. Oden, Contact problems in elasticity, SIAM, Philadelphia, 1988.
- P. D. Panagiotoupoulos and G. E. Stavroulakis, New types of variational principles based on the notion of quasi differentiability, Acta Mech. 94 (1992), 171-194. https://doi.org/10.1007/BF01176649
- A. Hassouni and A. Moudafi, A perturbed algorithms for variational inequalities, J. Math. Anal. Appl. 185 (1994), 706-712. https://doi.org/10.1006/jmaa.1994.1277
- X. P. Ding, Perturbed proximal point algorithms for generalized quasi variational inclusions, J. Math. Appl. Appl. 201 (1997), 88-101.
- X. P. Ding, Proximal point algorithm with errors for generalized strongly nonlinear quasi-variational inclusions, Appl. Math. Mech. 19 (7) (1998), 637-643. https://doi.org/10.1007/BF02452371
- X. P. Ding, On a class of generalized nonlinear implicit quasivariational inclusions, Appl. Math. Mech. 20 (10) (1999), 1087-1098. https://doi.org/10.1007/BF02460325
- X. P. Ding, Generalized implicit quasivariational inclusions with fuzzy set-valued mappings, Comput. Math. Appl. 38 (1) (1999), 71-79.
- X. P. Ding, Perturbed proximal point algorithms for general quasi-variational-like inclusions, J. Computat. Appl. Math. 113 (2000), 153-165. https://doi.org/10.1016/S0377-0427(99)00250-2
- X. P. Ding, Generalized quasi-variational-like inclusions with nonconvex functionals, Appl. Math. Comput. 122 (2001), 267-282.
- X. P. Ding, Perturbed Ishikawa Type Iterative Algorithm for Generalized Quasivariational Inclusions, Appl. Math. Comput. 14 (2003), 359-373.
- X. P. Ding, Algorithms of solutions for completely generalized mixed implicit quasivariational inclusions, Appl. Math. Comput. 148 (1) (2004), 47-66. https://doi.org/10.1016/S0096-3003(02)00825-1
- X. P. Ding, Predictor-Corrector iterative algorithms for solving generalized mixed quasi-variational-like inclusion, J. Comput. Appl. Math. 182 (1) (2005), 1-12. https://doi.org/10.1016/j.cam.2004.11.036
- X. P. Ding and Salahuddin, On a system of general nonlinear variational inclusions in Banach spaces, Appl. Math. Mech. 36 (12) (2015), 1663-1672, DOI:10.1007/s10483-015-1972-6.
-
X. P. Ding and H. R. Feng, The p-step iterative algorithm for a system of generalized mixed quasi-variational inclusions with (A,
$\eta$ )-accretive operators in q-uniformly smooth Banach spaces, J. Comput. Appl. Math. 220 (1-2) (2008), 163-174. https://doi.org/10.1016/j.cam.2007.08.003 - X. P. Ding and H. R. Feng, Algorithm for solving a new class of generalized nonlinear implicit quasi-variational inclusions in Banach spaces, Appl. Math. Comput. 208 (2009), 547-555.
-
X. P. Ding and Z. B. Wang, Sensitivity analysis for a system of parametric generalized mixed quasi-variational inclusions involving (K,
$\eta$ )-monotone mappings, Appl. Math. Comput. 214 (2009) 318-327. - X. P. Ding, Z. B. Wang, Auxiliary principle and algorithm for a system of generalized set-valued mixed variational-like inequality problems in Banach spaces, J. Comput. Appl. Math. 223 (2010), 2876-2883.
- Y. P. Fang and N. J. Huang, H-accretive operators and resolvent operators technique for solving variational inclusions in Banach spaces, Appl. Math. Lett. 17 (6) (2004), 647-653. https://doi.org/10.1016/S0893-9659(04)90099-7
-
X. He, On
$\phi$ -strongly accretive mapping and some set valued variational problems, J. Math. Anal. Appl. 277 (2) (2003), 504-511. https://doi.org/10.1016/S0022-247X(02)00582-6 - N. J. Huang, On the generalized implicit quasi variational inequalities, J. Math. Anal. Appl. 216 (1997), 197-210. https://doi.org/10.1006/jmaa.1997.5671
- J. S. Jung and C. H. Morales, The Mann process for perturbed m-accretive operators in Banach spaces, Nonlinear Anal. 46 (20) (2001), 231-243. https://doi.org/10.1016/S0362-546X(00)00115-2
- S. S. Chang, Set valued variational inclusions in Banach Spaces, J. Math. Anal. Appl. 248 (2000), 438-454. https://doi.org/10.1006/jmaa.2000.6919
- S. S. Chang, J. K. Kim and H. K. Kim, On the existence and iterative approximation problems of solutions for set valued variational inclusions in Banach spaces, J. Math. Anal. Appl. 268 (2002), 89-108. https://doi.org/10.1006/jmaa.2001.7800
- S. S. Chang, Y. J. Cho, B. S. Lee and I. J. Jung, Generalized set valued variational inclusions in Banach spaces, J. Math. Anal. Appl. 246 (2000), 409-422. https://doi.org/10.1006/jmaa.2000.6795
- S. S. Chang, Salahuddin and Y. K. Tang, A system of nonlinear set valued variational inclusions, SpringerPlus 2014, 3:318, Doi:10.1186/2193-180-3-318.
- S. S. Chang, Y. J. Cho, B. S. Lee, I. J. Jung and S. M. Kang, Iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo contractive mappings in Banach Spaces, J. Math. Anal. Appl. 224 (1998), 149-165. https://doi.org/10.1006/jmaa.1998.5993
- L. C. Ceng, S. S. Schaible and J. C. Yao, On the characterization of strong convergence of an iterative algorithm for a class of multivalued variational inclusions, Math. Math. Oper. Res. 70 (2009), 1-12. https://doi.org/10.1007/s00186-008-0227-8
- Y. J. Cho, H. Y. Zhou, S. M. Kang, S. S. Kim, Approximations for fixed points of -hemicontractive mappings by the Ishikawa iterative process with mixed errors, Math. Comput. Model. 34 (2001), 9-18. https://doi.org/10.1016/S0895-7177(01)00044-9
- C. E. Chidume, H. Zegeye and K.R. Kazmi, Existence and convergence theorem for a class of multivalued variational inclusions in Banach space, Nonlinear Anal. 59 (2004), 649-656. https://doi.org/10.1016/j.na.2004.06.003
- M. F. Khan and Salahuddin, Generalized multivalued nonlinear co-variational inequalities in Banach spaces, Funct. Diff. Equations 14 (2-4) (2007), 299-313.
- M. K. Ahmad and Salahuddin, Stable perturbed algorithms for a new class of generalized nonlinear implicit quasi variational inclusions in Banach spaces, Advances in Pure Math. 2 (2) (2012), 139-148. https://doi.org/10.4236/apm.2012.23021
- M. F. Khan and Salahuddin, Generalized co-complementarity problems in p-uniformly smooth Banach spaces, JIPAM, J. Inequal. Pure Appl. Math. 7 (2), Article 66, (2006), 11 pages.
- R. U. Verma and Salahuddin, Extended systems of nonlinear vector quasi variational inclusions and extended systems of nonlinear vector quasi optimization problems in locally FC-spaces, Commun. Appl. Nonlinear Anal. 23 (1) (2016), 71-88.
- Jr. S. B. Nadler, Multivalued contraction mappings, Pacific J. Math. 30 (1969), 475-487. https://doi.org/10.2140/pjm.1969.30.475
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