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Two mappings related to semi-inner products and their applications in geometry of normed linear spaces
Applications of Mathematics, Tome 45 (2000) no. 5, pp. 337-355 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we introduce two mappings associated with the lower and upper semi-inner product $(\cdot ,\cdot )_i$ and $(\cdot ,\cdot )_s$ and with semi-inner products $[\cdot ,\cdot ]$ (in the sense of Lumer) which generate the norm of a real normed linear space, and study properties of monotonicity and boundedness of these mappings. We give a refinement of the Schwarz inequality, applications to the Birkhoff orthogonality, to smoothness of normed linear spaces as well as to the characterization of best approximants.
In this paper we introduce two mappings associated with the lower and upper semi-inner product $(\cdot ,\cdot )_i$ and $(\cdot ,\cdot )_s$ and with semi-inner products $[\cdot ,\cdot ]$ (in the sense of Lumer) which generate the norm of a real normed linear space, and study properties of monotonicity and boundedness of these mappings. We give a refinement of the Schwarz inequality, applications to the Birkhoff orthogonality, to smoothness of normed linear spaces as well as to the characterization of best approximants.
DOI : 10.1023/A:1022268627299
Classification : 41A50, 46B20, 46B99, 46C50, 46C99
Keywords: lower and upper semi-inner product; semi-inner products; Schwarz inequality; smooth normed spaces; Birkhoff orthogonality; best approximants 
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Dragomir, S. S.; Koliha, J. J. Two mappings related to semi-inner products and their applications in geometry of normed linear spaces. Applications of Mathematics, Tome 45 (2000) no. 5, pp. 337-355. doi: 10.1023/A:1022268627299

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