Generalized Duality Mapping


  • AGH University of Science and Technology, Faculty of Applied Mathematics al., Krakow, 30-059, Poland
  • AGH University of Science and Technology, Faculty of Applied Mathematics, Krakow, 30-059, Poland


In this paper we propose a definition of generalized duality mapping, in short g.d.m. This definition is closely related to the classical definition of normalized duality mapping. We explore some properties of g.d.m. such as continuity, surjectivity and injectivity. In the terms of g.d.m. we prove more general results concerning strict convexity.


Duality Mapping, Normalized Duality Mapping, Semi-Inner Product, Semi-Inner Product Spaces.

Subject Discipline

Mathematical Sciences

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J. A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc., 40 (1936), 396–414.

S. Dragomir, Semi-inner Products and Applications, Nova Science Publishers, Hauppauge, New York, 2004.

G. D. Faulkner, Representation of linear functionals in a Banach space, Rocky Mountain J. Math., 7 (1977), 789–792.

J. R. Giles, Classes of semi-inner-product spaces, Trans. Amer. Math. Soc., 129 (1961), 436–446.

R. C. James, Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc., 61 (1947), 265–292.

J. Lindenstrauss and L. Tzafriri, Classical Banach spaces I, Bull. Amer. Math. Soc. (N.S.), 1 (1979), 230–232.

G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc., 100 (1961), 29–43.

A. Misiak, n-inner product spaces, Math. Nachr., 140 (1989), 299–319.

V. Smulian: Sur la d´erivabilit´e de la norme dans l’espace de Banach, Dokl. Akad. Nauk SSSR, 27 (1940), 643–648.

E. Torrance, Strictly convex spaces via semi-inner-product space orthogonality, Proc. Amer. Math. Soc., 26 (1970), 108–110.

H. Zhang and J. Zhang, Generalized Semi-inner Products and Applications to Regularized Learning, J. Math. Analysis and Appl., 372 (2010), 181–196.


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