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@article{DMDICO_2009_29_1_a0,
author = {Rolewicz, Stefan},
title = {How to define "convex functions" on differentiable manifolds},
journal = {Discussiones Mathematicae. Differential Inclusions, Control and Optimization},
pages = {7--17},
publisher = {mathdoc},
volume = {29},
number = {1},
year = {2009},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a0/}
}
TY - JOUR AU - Rolewicz, Stefan TI - How to define "convex functions" on differentiable manifolds JO - Discussiones Mathematicae. Differential Inclusions, Control and Optimization PY - 2009 SP - 7 EP - 17 VL - 29 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a0/ LA - en ID - DMDICO_2009_29_1_a0 ER -
%0 Journal Article %A Rolewicz, Stefan %T How to define "convex functions" on differentiable manifolds %J Discussiones Mathematicae. Differential Inclusions, Control and Optimization %D 2009 %P 7-17 %V 29 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a0/ %G en %F DMDICO_2009_29_1_a0
Rolewicz, Stefan. How to define "convex functions" on differentiable manifolds. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 29 (2009) no. 1, pp. 7-17. http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a0/
[1] [1] E. Asplund, Farthest points in reflexive locally uniformly rotund Banach spaces, Israel Jour. Math. 4 (1966), 213-216.
[2] [2] E. Asplund, Fréchet differentiability of convex functions, Acta Math. 121 (1968), 31-47.
[3] [3] S. Lang, Introduction to differentiable manifolds, Interscience Publishers (division of John Wiley Sons) New York, London, 1962.
[4] [4] S. Mazur, Über konvexe Mengen in linearen normierten Räumen, Stud. Math. 4 (1933), 70-84.
[5] [5] E. Michael, Local properties of topological spaces, Duke Math. Jour. 21 (1954), 163-174.
[6] [6] R.R. Phelps, Convex Functions, Monotone Operators and Differentiability, Lecture Notes in Mathematics, Springer-Verlag, 1364 (1989).
[7] [7] D. Preiss and L. Zajíček, Stronger estimates of smallness of sets of Fréchet nondifferentiability of convex functions, Proc. 11-th Winter School, Suppl. Rend. Circ. Mat di Palermo, ser II, 3 (1984), 219-223.
[8] [8] S. Rolewicz, On α(·)-monotone multifunction and differentiability of γ-paraconvex functions, Stud. Math. 133 (1999), 29-37.
[9] 9[] S. Rolewicz, On α(·)-paraconvex and strongly α(·)-paraconvex functions, Control and Cybernetics 29 (2000), 367-377.
[10] [10] S. Rolewicz, On the coincidence of some subdifferentials in the class of α(·)-paraconvex functions, Optimization 50 (2001), 353-360.
[11] [11] S. Rolewicz, On uniformly approximate convex and strongly α(·)-paraconvex functions, Control and Cybernetics 30 (2001), 323-330.
[12] [12] S. Rolewicz, α(·)-monotone multifunctions and differentiability of strongly α(·)-paraconvex functions, Control and Cybernetics 31 (2002), 601-619.
[13] [13] S. Rolewicz, On differentiability of strongly α(·)-paraconvex functions in non-separable Asplund spaces, Studia Math. 167 (2005), 235-244.
[14] [14] S. Rolewicz, Paraconvex analysis, Control and Cybernetics 34 (2005), 951-965.
[15] [15] S. Rolewicz, An extension of Mazur Theorem about Gateaux differentiability, Studia Math. 172 (2006), 243-248.
[16] [16] S. Rolewicz, Paraconvex Analysis on $C^{1,u}_E$-manifolds, Optimization 56 (2007), 49-60.
[17] [17] L. Zajicěk, Differentiability of approximately convex, semiconcave and strongly paraconvex functions, Jour. Convex Analysis 15 (2008), 1-15.