On directional derivatives for cone-convex functions

Krzysztof Leśniewski

DOI: http://dx.doi.org/10.12775/TMNA.2019.017

Abstract


We investigate the relationship between the existence of directional derivatives for cone-convex functions with values in a Banach space $Y$ and isomorphisms between $Y$ and $c_0$,

Keywords


Directional derivative; cone isomorphism; convex mappings; cone convex mappings

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References


F. Albiac and N.J. Kalton, Topics in Banach Spaces, Springer–Verlag, 2000.

Ch.D. Aliprantis and R. Tourky, Cones and Duality, Graduate Studies in Mathematics, Vol. 84, 2007.

E. Bednarczuk and K. Leśniewski, On weakly sequentially complete Banach spaces, J. Convex Anal 24 (2017), no. 4, 1341–1356.

Cz. Bessaga and A. Pelczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151–164.

E. Casini and E. Miglierina, Cones with bounded and unbounded bases and reflexivity, Nonlinear Anal. 72 (2010) , 2356–2366.

L.M. Graña Drummond, F.M.P. Raupp and B.F. Svaiter, A quadratically convergent Newton method for vector optimization, Optimization 63 (2014), no. 5, 661–677.

B.R. Gelbaum, Expansions in Banach spaces, Duke Math. J. 17 (1950), 187–196.

J. Jahn, Mathematical Vector Optimization in Partially Ordered Linear Spaces, Verlag Peter Lang, Frankfurt am Main, 1986.

J. Lindenstauss and L. Tzafriri, Classical Banach Spaces II, Springer–Verlag, 1979.

G.Ya. Lozanowskiı̆, Banach structures and bases, Funct. Anal. Appl. 1 (1967), 249. (in Russian)

C.W. McArthur, Developments in Schauder basis theory, Bull. Amer. Math. Soc. 78 (1972), no. 6, 877–908.

P. Meyer-Nieberg, Zur schwachen Kompaktheit in Banachverbänden, Math. Z. 134 (1973), 303–315.

T. Pennanen, Graph-convex mappings and K-convex functions, J. Convex Anal. 6 (1999), no. 2, 235–266.

A.L. Peressini, Ordered Topological Vector Spaces, Harper & Row, New York, Evanston, London, 1967.

I.A. Polyrakis, Cones Locally isomorphic to the Positive cone of l1 (Γ), Linear Algebra Appl. 44 (1986), 323–334.

I.A. Polyrakis, Cone characterization of reflexive Banach lattices, Glasg. Math. J. 37 (1995), 65–67.

I.A. Polyrakis and F. Xanthos, Cone characterization of Grothendieck spaces and Banach spaces containing c0 , Positivity 15 (2011), 677–693.

H. Rosenthal, A characterization of Banach spaces containing c0 , J. Amer. Math. Soc. 7 (1994), no. 7, 707–748.

I. Singer, Bases of Banach Spaces II, Springer, 1970.

P. Terenzi, Every separable Banach space has a bounded strong norming biorthogonal sequence which is also Steintz basis, Studia Math. 111 (1994), no. 3.

M. Valadier, Sous-Différentiabilité de fonctions convexes à valeurs dans un espace vectoriel ordonné, Math. Sand. 30 (1972), 65–74.


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