General implicit variational inclusion problems involving $A$-maximal relaxed accretive mappings in Banach spaces
Archivum mathematicum, Tome 45 (2009) no. 3, pp. 171-177 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 47J20, 47J25, 49J40, 65B05, 65J15
Keywords: implicit variational inclusions; maximal relaxed accretive mapping; $A$-maximal accretive mapping; generalized resolvent operator
@article{ARM_2009_45_3_a1,
     author = {Verma, Ram U.},
     title = {General implicit variational inclusion problems involving $A$-maximal relaxed accretive mappings in {Banach} spaces},
     journal = {Archivum mathematicum},
     pages = {171--177},
     year = {2009},
     volume = {45},
     number = {3},
     mrnumber = {2591673},
     zbl = {1212.49014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2009_45_3_a1/}
}
TY  - JOUR
AU  - Verma, Ram U.
TI  - General implicit variational inclusion problems involving $A$-maximal relaxed accretive mappings in Banach spaces
JO  - Archivum mathematicum
PY  - 2009
SP  - 171
EP  - 177
VL  - 45
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ARM_2009_45_3_a1/
LA  - en
ID  - ARM_2009_45_3_a1
ER  - 
%0 Journal Article
%A Verma, Ram U.
%T General implicit variational inclusion problems involving $A$-maximal relaxed accretive mappings in Banach spaces
%J Archivum mathematicum
%D 2009
%P 171-177
%V 45
%N 3
%U http://geodesic.mathdoc.fr/item/ARM_2009_45_3_a1/
%G en
%F ARM_2009_45_3_a1
Verma, Ram U. General implicit variational inclusion problems involving $A$-maximal relaxed accretive mappings in Banach spaces. Archivum mathematicum, Tome 45 (2009) no. 3, pp. 171-177. http://geodesic.mathdoc.fr/item/ARM_2009_45_3_a1/

[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. | MR | Zbl

[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. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[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. | MR | Zbl

[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. | DOI | MR | Zbl

[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. | DOI | MR

[7] Peng, J. W.: Set-valued variational inclusions with T-accretive operators in Banach spaces. Appl. Math. Lett. 19 (2006), 273–282. | DOI | MR | Zbl

[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. | MR | Zbl

[9] Verma, R. U.: $A$-monotonicity and its role in nonlinear variational inclusions. J. Optim. Theory Appl. 129 (3) (2006), 457–467. | DOI | MR | Zbl

[10] Verma, R. U.: Averaging techniques and cocoercively monotone mappings. Math. Sci. Res. J. 10 (3) (2006), 79–82. | MR | Zbl

[11] Verma, R. U.: General system of $A$-monotone nonlinear variational inclusion problems. J. Optim. Theory Appl. 131 (1) (2006), 151–157. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[13] Verma, R. U.: $A$-monotone nonlinear relaxed cocoercive variational inclusions. Cent. Eur. J. Math. 5 (2) (2007), 1–11. | DOI | MR | Zbl

[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

[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. | DOI | MR

[16] Verma, R. U.: Rockafellar’s celebrated theorem based on $A$-maximal monotonicity design. Appl. Math. Lett. 21 (2008), 355–360. | DOI | MR | Zbl

[17] Xu, H. K.: Iterative algorithms for nonlinear operators. J. London Math. Soc. (2) 66 (2002), 240–256. | DOI | MR | Zbl

[18] Zeidler, E.: Nonlinear Functional Analysis and its Applications I. Springer-Verlag, New York, 1986. | MR | Zbl

[19] Zeidler, E.: Nonlinear Functional Analysis and its Applications II/A. Springer-Verlag, New York, 1990. | MR | Zbl

[20] Zeidler, E.: Nonlinear Functional Analysis and its Applications II/B. Springer-Verlag, New York, 1990. | MR | Zbl