Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2016, Cilt: 4 Sayı: 4, 188 - 197, 31.12.2016

Öz

Kaynakça

  • 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.
  • H. H. Bauschke, X. Wang and L. Yao, On the maximal mono tonicity of the sum of a maximal monotone linear relation and the subdifferential operator of a sublinear function, Proceedings of the Haifa Workshop on Optimization Theory and Related Topics. Contemp. Math., Amer. Math. Soc., Providence, RI 568 (2012) 19-26.
  • J. M. Borwein, Maximality of sums of two maximal monotone operators in general Banach space, P. Am. Math. Soc. 135 (2007) 3917-3924.
  • 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.
  • J. M. Borwein and L. Yao, Structure theory for maximally monotone operators with points of continuity, J. Optim Theory Appl. 157 (2013) 1-24 http://dx.doi.org/10.1007/s10957-012-0162-y.
  • J.M. Borwein and L. Yao, Sum theorems for maximally monotone operators of type (FPV), J. Aust. Math. Soc. 97 (2014) 1-26.
  • S. Fitzpatrick, Representing monotone operators by convex functions, in Work- shop/Miniconference on Functional Analysis and Optimization (Canberra 1988), Proceedings of the Centre for Mathematical Analysis, Australian National University, Canberra, Australia, 20 (1988) 59-65.
  • R.R. Phelps, Convex Functions, Monotone Operators and Differentiability, 2nd Edition, Springer-Verlag, 1993.
  • R.T. Rockafellar, Local boundedness of nonlinear, monotone operators, Mich. Math. J. 16 (1969) 397-407.
  • R.T. Rockafellar, On the maximality of sums of nonlinear monotone operators, T. Am. Math. Soc. 149 (1970) 75-88.
  • R. Rudin, Functional Analysis, Second Edition, McGraw-Hill, 1991.
  • S. Simons, Minimax and Monotonicity, Springer-Verlag, 1998.
  • S. Simons, From Hahn-Banach to Monotonicity, Springer-Verlag, 2008.
  • M.D. Voisei, The sum and chain rules for maximal monotone operators, Set-Valued Var. Anal. 16 (2008) 461-476.
  • 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.
  • L. Yao, Maximality of the sum of the subdifferential operator and a maximally monotone operator, arXiv: 1406.7664v1[math.FA] 30 Jun 2014, http://arxiv.org/pdf/1406.7664.pdf.
  • C. Zalinescu, Convex Analysis in General Vector Spaces, World Scientific Publishing, 2002.

On sum of monotone operator of type (FPV) and a maximal monotone operator

Yıl 2016, Cilt: 4 Sayı: 4, 188 - 197, 31.12.2016

Öz


Kaynakça

  • 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.
  • H. H. Bauschke, X. Wang and L. Yao, On the maximal mono tonicity of the sum of a maximal monotone linear relation and the subdifferential operator of a sublinear function, Proceedings of the Haifa Workshop on Optimization Theory and Related Topics. Contemp. Math., Amer. Math. Soc., Providence, RI 568 (2012) 19-26.
  • J. M. Borwein, Maximality of sums of two maximal monotone operators in general Banach space, P. Am. Math. Soc. 135 (2007) 3917-3924.
  • 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.
  • J. M. Borwein and L. Yao, Structure theory for maximally monotone operators with points of continuity, J. Optim Theory Appl. 157 (2013) 1-24 http://dx.doi.org/10.1007/s10957-012-0162-y.
  • J.M. Borwein and L. Yao, Sum theorems for maximally monotone operators of type (FPV), J. Aust. Math. Soc. 97 (2014) 1-26.
  • S. Fitzpatrick, Representing monotone operators by convex functions, in Work- shop/Miniconference on Functional Analysis and Optimization (Canberra 1988), Proceedings of the Centre for Mathematical Analysis, Australian National University, Canberra, Australia, 20 (1988) 59-65.
  • R.R. Phelps, Convex Functions, Monotone Operators and Differentiability, 2nd Edition, Springer-Verlag, 1993.
  • R.T. Rockafellar, Local boundedness of nonlinear, monotone operators, Mich. Math. J. 16 (1969) 397-407.
  • R.T. Rockafellar, On the maximality of sums of nonlinear monotone operators, T. Am. Math. Soc. 149 (1970) 75-88.
  • R. Rudin, Functional Analysis, Second Edition, McGraw-Hill, 1991.
  • S. Simons, Minimax and Monotonicity, Springer-Verlag, 1998.
  • S. Simons, From Hahn-Banach to Monotonicity, Springer-Verlag, 2008.
  • M.D. Voisei, The sum and chain rules for maximal monotone operators, Set-Valued Var. Anal. 16 (2008) 461-476.
  • 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.
  • L. Yao, Maximality of the sum of the subdifferential operator and a maximally monotone operator, arXiv: 1406.7664v1[math.FA] 30 Jun 2014, http://arxiv.org/pdf/1406.7664.pdf.
  • C. Zalinescu, Convex Analysis in General Vector Spaces, World Scientific Publishing, 2002.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

D. K. Pradhan Bu kişi benim

S. R. Pattanaik Bu kişi benim

Yayımlanma Tarihi 31 Aralık 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 4

Kaynak Göster

APA Pradhan, D. K., & Pattanaik, S. R. (2016). On sum of monotone operator of type (FPV) and a maximal monotone operator. New Trends in Mathematical Sciences, 4(4), 188-197.
AMA Pradhan DK, Pattanaik SR. On sum of monotone operator of type (FPV) and a maximal monotone operator. New Trends in Mathematical Sciences. Aralık 2016;4(4):188-197.
Chicago Pradhan, D. K., ve S. R. Pattanaik. “On Sum of Monotone Operator of Type (FPV) and a Maximal Monotone Operator”. New Trends in Mathematical Sciences 4, sy. 4 (Aralık 2016): 188-97.
EndNote Pradhan DK, Pattanaik SR (01 Aralık 2016) On sum of monotone operator of type (FPV) and a maximal monotone operator. New Trends in Mathematical Sciences 4 4 188–197.
IEEE D. K. Pradhan ve S. R. Pattanaik, “On sum of monotone operator of type (FPV) and a maximal monotone operator”, New Trends in Mathematical Sciences, c. 4, sy. 4, ss. 188–197, 2016.
ISNAD Pradhan, D. K. - Pattanaik, S. R. “On Sum of Monotone Operator of Type (FPV) and a Maximal Monotone Operator”. New Trends in Mathematical Sciences 4/4 (Aralık 2016), 188-197.
JAMA Pradhan DK, Pattanaik SR. On sum of monotone operator of type (FPV) and a maximal monotone operator. New Trends in Mathematical Sciences. 2016;4:188–197.
MLA Pradhan, D. K. ve S. R. Pattanaik. “On Sum of Monotone Operator of Type (FPV) and a Maximal Monotone Operator”. New Trends in Mathematical Sciences, c. 4, sy. 4, 2016, ss. 188-97.
Vancouver Pradhan DK, Pattanaik SR. On sum of monotone operator of type (FPV) and a maximal monotone operator. New Trends in Mathematical Sciences. 2016;4(4):188-97.