| Title:
|
General implicit variational inclusion problems involving $A$-maximal relaxed accretive mappings in Banach spaces (English) |
| Author:
|
Verma, Ram U. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
171-177 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A class of existence theorems in the context of solving a general class of nonlinear implicit inclusion problems are examined based on $A$-maximal relaxed accretive mappings in a real Banach space setting. (English) |
| Keyword:
|
implicit variational inclusions |
| Keyword:
|
maximal relaxed accretive mapping |
| Keyword:
|
$A$-maximal accretive mapping |
| Keyword:
|
generalized resolvent operator |
| MSC:
|
47J20 |
| MSC:
|
47J25 |
| MSC:
|
49J40 |
| MSC:
|
65B05 |
| MSC:
|
65J15 |
| idZBL:
|
Zbl 1212.49014 |
| idMR:
|
MR2591673 |
| . |
| Date available:
|
2009-09-18T11:23:22Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134229 |
| . |
| Reference:
|
[1] Dhage, B. C., Verma, R. U.: Second order boundary value problems of discontinuous differential inclusions.Comm. Appl. Nonlinear Anal. 12 (3) (2005), 37–44. Zbl 1088.34505, MR 2142916 |
| Reference:
|
[2] Fang, Y. P., Huang, N. J.: $H$-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces.Appl. Math. Lett. 17 (2004), 647–653. Zbl 1056.49012, MR 2064175, 10.1016/S0893-9659(04)90099-7 |
| Reference:
|
[3] Fang, Y. P., Huang, N. J., Thompson, H. B.: A new system of variational inclusions with $(H,\eta )$-monotone operators.Comput. Math. Appl. 49 (2–3) (2005), 365–374. Zbl 1068.49003, MR 2123413, 10.1016/j.camwa.2004.04.037 |
| Reference:
|
[4] Huang, N. J., Fang, Y. P., Cho, Y. J.: Perturbed three-step approximation processes with errors for a class of general implicit variational inclusions.J. Nonlinear Convex Anal. 4 (2) (2003), 301–308. Zbl 1028.49006, MR 1999271 |
| Reference:
|
[5] Lan, H. Y., Cho, Y. J., Verma, R. U.: Nonlinear relaxed cocoercive variational inclusions involving $(A,\eta )$-accretive mappings in Banach spaces.Comput. Math. Appl. 51 (2006), 1529–1538. Zbl 1207.49011, MR 2237649, 10.1016/j.camwa.2005.11.036 |
| Reference:
|
[6] Lan, H. Y., Kim, J. H., Cho, Y. J.: On a new class of nonlinear $A$-monotone multivalued variational inclusions.J. Math. Anal. Appl. 327 (1) (2007), 481–493. MR 2277428, 10.1016/j.jmaa.2005.11.067 |
| Reference:
|
[7] Peng, J. W.: Set-valued variational inclusions with T-accretive operators in Banach spaces.Appl. Math. Lett. 19 (2006), 273–282. Zbl 1102.47050, MR 2202416, 10.1016/j.aml.2005.04.009 |
| Reference:
|
[8] Verma, R. U.: On a class of nonlinear variational inequalities involving partially relaxed monotone and partially strongly monotone mappings.Math. Sci. Res. Hot-Line 4 (2) (2000), 55–63. Zbl 1054.49010, MR 1742730 |
| Reference:
|
[9] Verma, R. U.: $A$-monotonicity and its role in nonlinear variational inclusions.J. Optim. Theory Appl. 129 (3) (2006), 457–467. Zbl 1123.49007, MR 2281151, 10.1007/s10957-006-9079-7 |
| Reference:
|
[10] Verma, R. U.: Averaging techniques and cocoercively monotone mappings.Math. Sci. Res. J. 10 (3) (2006), 79–82. Zbl 1152.49011, MR 2231178 |
| Reference:
|
[11] Verma, R. U.: General system of $A$-monotone nonlinear variational inclusion problems.J. Optim. Theory Appl. 131 (1) (2006), 151–157. Zbl 1107.49012, MR 2278302, 10.1007/s10957-006-9133-5 |
| Reference:
|
[12] Verma, R. U.: Sensitivity analysis for generalized strongly monotone variational inclusions based on the $(A,\eta )$-resolvent operator technique.Appl. Math. Lett. 19 (2006), 1409–1413. Zbl 1133.49014, MR 2264199, 10.1016/j.aml.2006.02.014 |
| Reference:
|
[13] Verma, R. U.: $A$-monotone nonlinear relaxed cocoercive variational inclusions.Cent. Eur. J. Math. 5 (2) (2007), 1–11. Zbl 1128.49011, MR 2300280, 10.2478/s11533-007-0005-5 |
| Reference:
|
[14] Verma, R. U.: General system of $(A,\eta )$-monotone variational inclusion problems based on generalized hybrid algorithm.Nonlinear Anal. Hybrid Syst. 1 (3) (2007), 326–335. MR 2339479 |
| Reference:
|
[15] Verma, R. U.: Aproximation solvability of a class of nonlinear set-valued inclusions involving $(A,\eta )$-monotone mappings.J. Math. Anal. Appl. 337 (2008), 969–975. MR 2386346, 10.1016/j.jmaa.2007.01.114 |
| Reference:
|
[16] Verma, R. U.: Rockafellar’s celebrated theorem based on $A$-maximal monotonicity design.Appl. Math. Lett. 21 (2008), 355–360. Zbl 1148.47039, MR 2406513, 10.1016/j.aml.2007.05.004 |
| Reference:
|
[17] Xu, H. K.: Iterative algorithms for nonlinear operators.J. London Math. Soc. (2) 66 (2002), 240–256. Zbl 1013.47032, MR 1911872, 10.1112/S0024610702003332 |
| Reference:
|
[18] Zeidler, E.: Nonlinear Functional Analysis and its Applications I.Springer-Verlag, New York, 1986. Zbl 0583.47050, MR 0816732 |
| Reference:
|
[19] Zeidler, E.: Nonlinear Functional Analysis and its Applications II/A.Springer-Verlag, New York, 1990. Zbl 0684.47028, MR 1033497 |
| Reference:
|
[20] Zeidler, E.: Nonlinear Functional Analysis and its Applications II/B.Springer-Verlag, New York, 1990. Zbl 0684.47029, MR 1033498 |
| . |
