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Geometric properties and continuity of the pre-duality mapping in Banach space

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Geometric properties and continuity of the pre-duality mapping in Banach space

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Zhang, ZH.; Montesinos Santalucia, V.; Liu, CY.; Gong, WZ. (2015). Geometric properties and continuity of the pre-duality mapping in Banach space. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas. 109(2):407-416. https://doi.org/10.1007/s13398-014-0190-6

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Título: Geometric properties and continuity of the pre-duality mapping in Banach space
Autor: Zhang, Z. H. Montesinos Santalucia, Vicente Liu, C. Y. Gong, W. Z.
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
We use the preduality mapping in proving characterizations of some geometric properties of Banach spaces. In particular, those include nearly strongly convexity, nearly uniform convexity-a property introduced by K. Goebel ...[+]
Palabras clave: Duality mapping , Pre-duality mapping , Alpha-upper semi-continuity , Usco mapping , Nearly strongly convex space , Nearly uniformly convex space , Nearly very convex space
Derechos de uso: Reserva de todos los derechos
Fuente:
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas. (issn: 1578-7303 )
DOI: 10.1007/s13398-014-0190-6
Editorial:
Springer
Versión del editor: http://dx.doi.org/10.1007/s13398-014-0190-6
Código del Proyecto:
info:eu-repo/grantAgreement/NSFC//11271248/
info:eu-repo/grantAgreement/MICINN//MTM2011-22417/ES/ESPACIOS Y ALGEBRAS DE FUNCIONES DIFERENCIABLES/
info:eu-repo/grantAgreement/SMEC//B-8932-13-0136/
Agradecimientos:
We thank a referee for the careful reading of the manuscript. His/her observations substantially improved the overall aspect of the present work, detected several misprints and made some convenient changes. This work was ...[+]
Tipo: Artículo

References

Bandyopadhyay, P., Huang, D., Lin, B.L., Troyanski, S.L.: Some generalizations of local uniform rotundity. J. Math. Anal. Appl. 252, 906–916 (2000)

Bandyopadhyay, P., Li, Y., Lin, B., Narayana, D.: Proximinality in Banach spaces. J. Math. Anal. Appl. 341, 309–317 (2008)

Diestel, J.: Geometry of Banach Spaces. Selected Topics, LNM, vol. 485. Springer, Berlin (1975) [+]
Bandyopadhyay, P., Huang, D., Lin, B.L., Troyanski, S.L.: Some generalizations of local uniform rotundity. J. Math. Anal. Appl. 252, 906–916 (2000)

Bandyopadhyay, P., Li, Y., Lin, B., Narayana, D.: Proximinality in Banach spaces. J. Math. Anal. Appl. 341, 309–317 (2008)

Diestel, J.: Geometry of Banach Spaces. Selected Topics, LNM, vol. 485. Springer, Berlin (1975)

Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V.: Banach Space Theory. The Basis for Linear and Nonlinear Analysis, CMS Books in Mathematics. Springer, Berlin (2011)

Giles, J.R., Gregory, D.A., Sims, B.: Geometrical implications of upper semi-continuity of the duality mapping on a Banach space. Pacific J. Math. 79(1), 99–109 (1978)

Goebel, K., Sekowski, T.: The modulus of non-compact convexity. Ann. Univ. M. Curie-Sklodowska, Sect. A 38, 41–48 (1984)

Guirao, A.J., Montesinos, V.: A note in approximative compactness and continuity of metric projections in Banach spaces. J. Convex Anal. 18, 397–401 (2011)

Huff, R.: Banach spaces which are nearly uniformly convex. Rocky Mountain J. Math. 10(4), 743–749 (1980)

Kutzarova, D., Rolewicz, S.: On nearly uniformly convex sets. Arch. Math. 57, 385–394 (1991)

Kutzarova, D., Lin, B.L., Zhang, W.: Some geometrical properties of Banach spaces related to nearly uniform convexity. Contemp. Math. 144, 165–171 (1993)

Kutzarova, D., Prus, S.: Operators which factor through nearly uniformly convex spaces. Boll. Un. Mat. Ital. B (7) 9, 2, 479–494 (1995)

Montesinos, V.: Drop property equals reflexivity. Studia Math. 87, 93–100 (1987)

Phelps, R.R.: Convex Functions, Monotone Operators and Differentiability, LNM, vol. 1364, 2nd edn. Springer, Berlin (1993)

Rolewicz, S.: On drop property. Studia Math. 85, 27–37 (1986)

Rolewicz, S.: On $$\Delta $$ Δ -uniform convexity and drop property. Studia Math. 87, 181–191 (1987)

Wu, C.X., Li, Y.J.: Strong convexity in Banach spaces. J. Math. Wuhan Univ. 13(1), 105–108 (1993)

Wang, J.H., Nan, C.X.: The continuity of subdifferential mapping. J. Math. Anal. Appl. 210, 206–214 (1997)

Wang, J.H., Zhang, Z.H.: Characterization of the property (C-K). Acta Math. Sci. Ser. A Chin. Ed. 17(A)(3), 280–284 (1997)

Zhang, Z.H., Liu, C.Y.: Some generalization of locally and weakly locally uniformly convex space. Nonlinear Anal. 74(12), 3896–3902 (2011)

Zhang, Z.H., Liu, C.Y.: Convexity and proximinality in Banach spaces. J. Funct. Spaces Appl. 2012, 11 (2012). doi: 10.1155/2012/724120 . Article ID 724120

Zhang, Z.H., Liu, C.Y.: Convexity and existence of the farthest point. Abstract Appl. Anal. 2011, 9 (2011). doi: 10.1155/2011/139597 . Article ID 139597

Zhang, Z.H., Shi, Z.R.: Convexities and approximative compactness and continuity of the metric projection in Banach spaces. J. Approx. Theory 161(2), 802–812 (2009)

Zhang, Z.H., Zhang, C.J.: On very rotund Banach spaces. Appl. Math. Mech. (English Ed.) 21(8), 965–970 (2000)

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