50
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Paraconvex analysis on -manifolds

Pages 49-60 | Received 12 Apr 2005, Accepted 23 Apr 2005, Published online: 13 Oct 2011

References

  • Asplund , E . 1966 . Farthest points in reflexive locally uniformly rotund Banach spaces . Israel Journal of Mathematics , 4 : 213 – 216 .
  • Asplund , E . 1968 . Fréchet differentiability of convex functions . Acta Mathematica , 121 : 31 – 47 .
  • Ioffe , AD . 1984 . Approximate subdifferentials and applications I . Transactions of the American Mathematical Society , 281 : 389 – 416 .
  • Ioffe , AD . 1986 . Approximate subdifferentials and applications II . Mathematika , 33 : 111 – 128 .
  • Ioffe , AD . 1989 . Approximate subdifferentials and applications III . Mathematika , 36 : 1 – 38 .
  • Ioffe , AD . 1990 . Proximal analysis and approximate subdifferentials . Journal of the London Mathematical Society , 41 : 175 – 192 .
  • Ioffe , AD . 2000 . Metric regularity and subdifferential calculus (in Russian) . Uspekhi Matematiticeskid Nauk , 55 ( 3 ) : 104 – 162 .
  • Lang , S . 1962 . Introduction to Differentiable Manifolds , New York, London : Interscience Publishers (division of John Wiley & Sons .
  • Luc , DT , Ngai , HV and Théra , M . 2000 . “ On ϵ-convexity and ϵ-monotonicity ” . In Calculus of Variation and Differential Equations , Edited by: Ioffe , A , Reich , S and Shafrir , I . Vol. 410 , 82 – 100 . Boca Raton, Raton, FL : Chapman & Hall/CRC . Research Notes in Mathematics Series
  • Luc , DT , Ngai , HV and Théra , M . 2000 . Approximate convex functions . Journal of Nonlinear and Convex Analysis , 1 : 155 – 176 .
  • Mazur , S . 1933 . Über konvexe Mengen in linearen normierten Räumen . Studia Mathematica , 4 : 70 – 84 .
  • Michael , E . 1954 . Local properties of topological spaces . Duke Mathematical Journal , 21 : 163 – 174 .
  • Mordukhovich , BS . 1976 . Maximum principle in the optimal control problems with non-smooth constraints (in Russian) . Prikladnoi Matematiki i Mehkhaniki , 40 : 1014 – 1023 .
  • Mordukhovich , BS . 1980 . Metric approximations and necessary optimality conditions for general classes of nonsmooth extremal problems (in Russian) . Soviet Math. Doklady , 254 : 1072 – 1076 . In English version (Translation) Mathematical 22, 526–530
  • Mordukhovich , BS . 1988 . Approximation Methods in Problems of Optimization and Control , Moscow, , Russian : Nauka .
  • Mordukhovich , BS . 2005 . Variational Analysis and Generalized Differentiation. Vol. 1. Basic Theory, Grundlehren der Mathematischen Wissenschaften , 330 Berlin, Heidelberg, New York : Springer-Verlag .
  • Mordukhovich , BS . 2005b . Variational Analysis and Generalized Differentiation. Vol. 2. Applications, Grundlehren der Mathematischen Wissenschaften , 331 Berlin, Heidelberg, New York : Springer-Verlag .
  • Phelps , RR . 1989 . Convex Functions, Monotone Operators and Differentiability , 1364 Berlin, Heidelberg, New York : Springer-Verlag . Lecture Notes in Mathematics
  • Preiss , D and Zajíček , L . 1984 . Stronger estimates of smallness of sets of Fréchet nondifferentiability of convex functions . Proceedings of 11th Winter School, Supplement to Rendicouti del Circole di Mathematica di Palermo, Ser II , 3 : 219 – 223 .
  • Rolewicz , S . 1999 . On α (·)-monotone multifunction and differentiability of γ-paraconvex functions . Studia Mathematica , 133 : 29 – 37 .
  • Rolewicz , S . 2000 . On α (·)-paraconvex and strongly α (·)-paraconvex functions . Control and Cybernetics , 29 : 367 – 377 .
  • Rolewicz , S . 2001 . On the coincidence of some subdifferentials in the class of α (·)-paraconvex functions . Optimization , 50 : 353 – 360 .
  • Rolewicz , S . 2001 . On uniformly approximate convex and strongly α (·)-para- convex functions . Control and Cybernetics , 30 : 323 – 330 .
  • Rolewicz , S . 2002 . α (·)-monotone multifunctions and differentiability of strongly α (·)-paraconvex functions. . Control and Cybernetics , 31 : 601 – 619 .
  • Rolewicz , S . 2005 . On differentiability of strongly α (·)-paraconvex functions in non-separable Asplund spaces . Studia Mathematica , 167 : 235 – 244 .
  • Rolewicz , S . 2005 . Paraconvex Analysis . Control and Cybernetics , 34 : 951 – 965 .
  • Rolewicz , S . 2006 . An extension of Mazur Theorem about Gateaux differentiability . Studia Mathematica , 172 : 197 – 205 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.