پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 697 |
| تعداد مقالات | 10,088 |
| تعداد مشاهده مقاله | 71,229,043 |
| تعداد دریافت فایل اصل مقاله | 62,958,127 |
On sum of range sets of sum of two maximal monotone operators | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 75، دوره 12، شماره 1، مرداد 2021، صفحه 927-934 اصل مقاله (399.01 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2019.12171.1615 | ||
| نویسندگان | ||
| Dillip Kumar Pradhan* ؛ Suvendu Ranjan Pattanaik | ||
| Department of Mathematics, National Institute of Technology, Rourkela, India | ||
| تاریخ دریافت: 14 مرداد 1396، تاریخ بازنگری: 21 آبان 1398، تاریخ پذیرش: 24 آبان 1398 | ||
| چکیده | ||
| In the setting of non-reflexive spaces (Grothendieck Banach spaces), we establish (1) $\overline{ran (A+B)}=\overline{ran A+ran B}$ (2) int (ran (A+B))=int(ran A+ran B). with the assumption that A is a maximal monotone operator and B is a single-valued maximal monotone operator such that A+B is ultramaximally monotone. Conditions (1) and (2) are known as Br$\acute{e}$zis-Haraux conditions. | ||
| کلیدواژهها | ||
| Monotone Operator؛ Maximal Monotone Operator؛ Ultramaximal Monotone Operator؛ Br$\acute{e}$zis-Haraux conditions | ||
| مراجع | ||
|
[1] A.R. Aftabizadeh and N. H. Pavel, Nonlinear boundary value problems for some ordinary and partial differential equations associated with monotone operators, J. Math. Anal. 156 (1991) 535-557. [2] N.C. Apreutesei, Second order differential equations on half-line associated with monotone operators, J. Math. Anal. 223 (1998) 472-493. [3] H.H. Bauschke, X. Wang and L. Yao, An answer to S. Simons’ question on the maximal monotonicity of the sum of a maximal monotone linear operator and a normal cone operator, Set-Valued Var. Anal. 17 (2009) 195-201. [4] H.H. Bauschke, X. Wang and L. Yao, On the maximal monotonicity of the sum of a maximal monotone linear relation and the subdifferential operator of a sublinear function, Proc. Haifa Workshop Optim. Theory Related Topics. Contemp. Math., Amer. Math. Soc., Providence, RI 568 (2012), pp. 19-26. [5] H.H. Bauschke and S. Simons, Stronger maximal monotonicity properties of linear operators, Bull. Aust. Math. Soc. 60 (1999) 163-174. [6] J. M. Borwein, Maximality of sums of two maximal monotone operators in general Banach space, Proc. Amer. Math. Soc. 135 (2007) 3917-3924. [7] J.M. Borwein and L. Yao, Maximality of the sum of a maximally monotone linear relation and a maximally monotone operator, Set-Valued Var. Anal. 21 (2013) 603-616. [8] J.M. Borwein and L. Yao, Sum theorems for maximally monotone operators of type (FPV), J. Aust. Math. Soc. 97 (2014) 1-26. [9] H. Brezis, Monotone operators, nonlinear semigroups, and applications, Proc. Int. Congress Math. Vancouver, 1974, pp. 249-255. [10] H. Brezis and F. Browder, Euations integrales non lineaires du type Hammerstein, C.R. Acad. Sci. Pari 279 (1974) 1-2. [11] H. Brezis and A. Haraux, Image d’une somme d’operateurs monotones et applications, Israel J. Math. 23 (1976) 165-186. [12] H. Brezis, M.G. Crandall and A. Pazy, Perturbations of Nonlinear Maximal Monotone Sets in Banach Spaces, Commun. Pure Appl. Math. XXIII (1970) 123-144. [13] F.E. Browder, On a principle of H. Brezis and its applications, J. Funct. Anal. 25 (1997) 356-365. [14] B.D. Calvert and C.P. Gupta, Nonlinear elliptic boundary value problems in Lp spaces and sums of ranges of accretive operators, Nonlinear Anal. 2 (1978) 1-26. [15] J.-P. Gossez, On a convexity property of the range of a maximal monotone operator, Proc. Amer. Math. Soc. 55 (1976) 359-360. [16] C.P. Gupta, Sum of ranges of operators and applications, Nonlinear Syst. Appl., 547-559, Academic Press, New York, 1997. [17] C.P. Gupta and P. Hess, Existence theorems for nonlinear noncoercieve operator equations and nonlinear elliptic boundary value problems, J. Differ. Equ. 22 (1976) 305-313. [18] G.J. Minty, Monotone Networks, Proc. Roy Soc. London. 257 (1960) 194-212. [19] T. J. Morrison, Functional Analysis: An Introduction to Banach Space Theory, A Wiley Intercedence publication, Jhon Wiley and Sons, New York, 2001. [20] S. Reich, The range of sums of accretive and monotone operators, J. Math. Anal. Appl. 68 (1979) 310-317. [21] R.T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc. 149 (1970) 75-88. [22] S. Simons, The range of a monotone operator, J. Math. Anal. Appl. 199 (1996) 176-201.
[24] S. Simons, From Hahn-Banach to Monotonicity, Springer-Verlag, 2008. [25] M.D. Voisei, The sum and chain rules for maximal monotone operators, Set-Valued Var. Anal. 16 (2008) 461-476. [26] L. Yao, Finer properties of ultra maximally monotone operators on Banach spaces, J. Convex Anal. 23 (2016) 1205-1218. [27] L. Yao, The sum of a maximally monotone linear relation and the subdifferential of a proper lower semicontinuous convex function is maximally monotone, Set-Valued Var. Anal. 20 (2012) 155-167. [28] L. Yao, Maximality of the sum of the subdifferential operator and a maximally monotone operator, Linear Nonlinear Anal. 1 (2018) 95-108. [29] E. Zeidler, Nonlinear Functional Analysis and Its Applications: Part 2 A: Linear Monotone Operators and Part 2 B: Nonlinear Monotone Operators, Springer-Verlag, 1990. | ||
|
آمار تعداد مشاهده مقاله: 15,941 تعداد دریافت فایل اصل مقاله: 9,519 |
||