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Article
Author(s)
N. K. Sahu
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DOI:10.17265/2159-5291/2015.06.006
Affiliation(s)
Dhirubhai Ambani Institute of Information and Communication Technology
ABSTRACT
KEYWORDS
Semi-inner product space, Generalized resolvent operator, Variational inclusion, 2-uniformly smooth Banach space.
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References
[1] S. Adly, Perturbed algorithm and sensitivity analysis for a general class of variational inclusions, J. Math. Anal. Appl. 201 (1996), 609-630.
[2] R. P. Agarwal and R. U. Verma, General system of (A,η)-maximal relaxed monotone variational inclusion problems based on generalized hybrid algorithms, Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 238-251.
[3] R. Ahmad, M. Akram and J. C. Yao, Generalized monotone mapping with an application for solving a variational inclusion problem, J. Optim. Theory Appl. 157(2) (2013), 324-346.
[4] X. P. Ding, Perturbed proximal point for generalized quasi-variational inclusions, J. Math. Anal. Appl. 210 (1997), 88-101.
[5] X. P. Ding and C. L. Luo, Perturbed proximal point algorithms for generalized quasi-variational like inclusions, J. Comput. Appl. Math. 210 (2000), 153-165.
[6] Y. P. Fang and N. J. Huang, H-monotone operator and resolvent operator technique for variational inclusions, Appl. Math. Comput. 145 (2003), 795-803.
[7] J. R. Giles, Classes of semi-inner product spaces, Trans. Amer. Math. Soc. 129 (1967), 436-446.
[8] N. J. Huang, A new class of generalized set valued implicit variational inclusions in Banach spaces with an application, Comput. Math. Appl. 41 (2001), 937-943.
[9] M. M. Jin, Iterative algorithm for a new system of nonlinear set-valued variational inclusions involving (H,η)-monotone mappings, J. Inequal. Pure Appl. Math. 7(2) (2006), Article 72.
[10] D. O. Koehler, A note on some operator theory in certain semi-inner product spaces, Proc. Amer. Math. Soc. 30(2) (1971), 363-366.
[11] H. Y. Lan, J. H. Kim and Y. J. Cho, On a new system of nonlinear A-monotone multivalued variational inclusions, J. Math. Anal. Appl. 327 (2007), 481-493.
[12] C. H. Lee, Q. H. Ansari and J. C. Yao, A perturbed algorithm for strongly nonlinear variational like inclusions, Bull. Aust. Math. Soc. 62 (2000), 417-426.
[13] G. Lumer, Semi-inner product spaces, Trans. Amer. Math. Soc. 100 (1961), 29-43.
[14] A. Moudafi, Split monotone variational inclusions, J. Optim. Theory Appl. 150(2) (2011), 275-283.
[15] M. A. Noor, K. I. Noor and R. Kamal, General variational inclusions involving difference of operators, J. Inequal. Appl. 2014(1) (2014), Article ID 98.
[16] J. Peng and D. Zhu, A new system of generalized mixed quasi-variational inclusions with (H,η)-monotone operators, J. Math. Anal. Appl. 327 (2007), 175-187.
[17] N. K. Sahu, R. N. Mohapatra, C. Nahak and S. Nanda, Approximation solvability of a class of A-monotone implicit variational inclusion problems in semi-inner product spaces, Appl. Math. Comput. 236 (2014), 109-117.
[18] R. U. Verma, General nonlinear variational inclusion problems involving A-monotone mappings, Appl. Math. Lett., , (2006) 960-963.
[19] R. U. Verma, Approximation solvability of a class of nonlinear set-valued variational inclusions involving (A,η)-monotone mappings, J. Math. Anal. Appl. 337 (2008), 969-975.
[20] R. U. Verma, Sensitivity analysis for generalized strongly monotone variational inclusions based on (A,η)-resolvent operator technique, Appl. Math. Lett. 19 (2006), 1409-1413.
[21] R. U. Verma, A-monotonicity and its role in nonlinear variational inclusions, J. Optim. Theory Appl. 129(3) (2006), 457-467.
[22] R. U. Verma, General class of implicit variational inclusions and graph convergence on A-maximal relaxed monotonicity, J. Optim. Theory Appl., 155 (1), (2012), 196-214.
[23] H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Analysis: Theory, Methods and Applications 16(12) (1991), 1127-1138.
[2] R. P. Agarwal and R. U. Verma, General system of (A,η)-maximal relaxed monotone variational inclusion problems based on generalized hybrid algorithms, Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 238-251.
[3] R. Ahmad, M. Akram and J. C. Yao, Generalized monotone mapping with an application for solving a variational inclusion problem, J. Optim. Theory Appl. 157(2) (2013), 324-346.
[4] X. P. Ding, Perturbed proximal point for generalized quasi-variational inclusions, J. Math. Anal. Appl. 210 (1997), 88-101.
[5] X. P. Ding and C. L. Luo, Perturbed proximal point algorithms for generalized quasi-variational like inclusions, J. Comput. Appl. Math. 210 (2000), 153-165.
[6] Y. P. Fang and N. J. Huang, H-monotone operator and resolvent operator technique for variational inclusions, Appl. Math. Comput. 145 (2003), 795-803.
[7] J. R. Giles, Classes of semi-inner product spaces, Trans. Amer. Math. Soc. 129 (1967), 436-446.
[8] N. J. Huang, A new class of generalized set valued implicit variational inclusions in Banach spaces with an application, Comput. Math. Appl. 41 (2001), 937-943.
[9] M. M. Jin, Iterative algorithm for a new system of nonlinear set-valued variational inclusions involving (H,η)-monotone mappings, J. Inequal. Pure Appl. Math. 7(2) (2006), Article 72.
[10] D. O. Koehler, A note on some operator theory in certain semi-inner product spaces, Proc. Amer. Math. Soc. 30(2) (1971), 363-366.
[11] H. Y. Lan, J. H. Kim and Y. J. Cho, On a new system of nonlinear A-monotone multivalued variational inclusions, J. Math. Anal. Appl. 327 (2007), 481-493.
[12] C. H. Lee, Q. H. Ansari and J. C. Yao, A perturbed algorithm for strongly nonlinear variational like inclusions, Bull. Aust. Math. Soc. 62 (2000), 417-426.
[13] G. Lumer, Semi-inner product spaces, Trans. Amer. Math. Soc. 100 (1961), 29-43.
[14] A. Moudafi, Split monotone variational inclusions, J. Optim. Theory Appl. 150(2) (2011), 275-283.
[15] M. A. Noor, K. I. Noor and R. Kamal, General variational inclusions involving difference of operators, J. Inequal. Appl. 2014(1) (2014), Article ID 98.
[16] J. Peng and D. Zhu, A new system of generalized mixed quasi-variational inclusions with (H,η)-monotone operators, J. Math. Anal. Appl. 327 (2007), 175-187.
[17] N. K. Sahu, R. N. Mohapatra, C. Nahak and S. Nanda, Approximation solvability of a class of A-monotone implicit variational inclusion problems in semi-inner product spaces, Appl. Math. Comput. 236 (2014), 109-117.
[18] R. U. Verma, General nonlinear variational inclusion problems involving A-monotone mappings, Appl. Math. Lett., , (2006) 960-963.
[19] R. U. Verma, Approximation solvability of a class of nonlinear set-valued variational inclusions involving (A,η)-monotone mappings, J. Math. Anal. Appl. 337 (2008), 969-975.
[20] R. U. Verma, Sensitivity analysis for generalized strongly monotone variational inclusions based on (A,η)-resolvent operator technique, Appl. Math. Lett. 19 (2006), 1409-1413.
[21] R. U. Verma, A-monotonicity and its role in nonlinear variational inclusions, J. Optim. Theory Appl. 129(3) (2006), 457-467.
[22] R. U. Verma, General class of implicit variational inclusions and graph convergence on A-maximal relaxed monotonicity, J. Optim. Theory Appl., 155 (1), (2012), 196-214.
[23] H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Analysis: Theory, Methods and Applications 16(12) (1991), 1127-1138.