A relational reformulation of the Phelps–Cardwell lemma
Downloads
DOI:
https://doi.org/10.26637/mjm203/011Abstract
By using some results on translation and superadditive relations, we give some relational reformulations of the Phelps–Cardwell lemma in terms of open and closed surroundings. These reformulations have mainly been suggested by a unifying scheme for continuities of relations in relator spaces and a projective generation of translation relators by superadditive relations.
Keywords:
Translation and superadditive relations, open and closed surroundings, Phelps–Cardwell lemmaMathematics Subject Classification:
46B20, 47A07, 08A02, 54E15- Pages: 254-262
- Date Published: 01-07-2014
- Vol. 2 No. 03 (2014): Malaya Journal of Matematik (MJM)
R. Aron, A. Cardwell, D. Garc´ ıa, and I. Zalduendo, A multilinear Phelps’ lemma, Proc. Amer. Math. Soc. 135(2007), 2549–2554. DOI: https://doi.org/10.1090/S0002-9939-07-08762-X
E. Bishop and R.R. Phelps, A proof that every Banach space is subreflexive, Bull. Amer. Math. Soc. 67(1961), 97–98. DOI: https://doi.org/10.1090/S0002-9904-1961-10514-4
A.E. Cardwell, A new proof of a lemma by Phelps, Int. J. Math. Math. Sci. 2006, Art. ID 28063, 3 pp. DOI: https://doi.org/10.1155/IJMMS/2006/28063
M. Fabian, P. Habala, P. Hájek, J. Pelant, V. Montesinos and V. Zizler, Functional Analysis and Infinite Dimensional Geometry, Canad. Math. Soc. Books in Math., Springer-Verlag, New York, 2001. DOI: https://doi.org/10.1007/978-1-4757-3480-5
M. Fabian, V. Montesinos and V. Zizler, A characterization of subspaces of weakly compactly generated Banach spaces, J. London Math. Soc. 69(2004), 457-464. DOI: https://doi.org/10.1112/S0024610703005118
T. Glavosits and A. Száz, On the existence of odd selections, Adv. Stud. Contemp. Math. (Kyungshang) 8(2004), 155–164.
T. Glavosits and A. Száz, Constructions and extensions of free and controlled additive relations, Tech. Rep., Inst. Math., Univ. Debrecen 2010/1, 49 pp.
G. Pataki and A. Száz, A unified treatment of well-chainedness and connectedness properties, Acta Math. Acad. Paedagog. Nyházi. (N.S.) 19(2003), 101–165.
R.R. Phelps, A representation theorem for bounded convex sets, Proc. Amer. Math. Soc. 11(1960), 976–983. DOI: https://doi.org/10.1090/S0002-9939-1960-0123172-X
A. Száz, Projective generation of preseminormed spaces by linear relations, Studia Sci. Math. Hungar. 23(1988), 297–313.
A. Száz, Projective and inductive generations of relator spaces, Acta Math. Hungar. 53(1989), 407–430. DOI: https://doi.org/10.1007/BF01953378
A. Száz, The intersection convolution of relations and the Hahn–Banach type theorems, Ann. Polon. Math. 69(1998), 235–249. DOI: https://doi.org/10.4064/ap-69-3-235-249
A. Száz, Translation relations, the building blocks of compatible relators, Math. Montisnigri 12(2000), 135–156.
A. Száz, Preseminorm generating relations and their Minkowski functionals, Univ. Beograd., Publ. Elektotechn. Fak., Ser. Mat. 12(2001), 16–34.
A. Száz, Somewhat continuity in a unified framework for continuities of relations, Tatra Mt. Math. Publ. 24(2002), 41–56.
A. Száz, Relationships between translation and additive relations, Acta Acad. Paedagog. Agriensis, Sect. Math. (N.S.) 30(2003), 179–190.
A. Száz, Foundations of the theory of vector relators, Adv. Stud. Contemp. Math. (Kyungshang) 20(2010), 139–195.
A. Száz, The Hyers–Ulam and Hahn–Banach theorems and some elementary operations on relations motivated their set-valued generalizations In: P.M. Pardalos, P.G. Georgiev and H.M. Srivastava (eds.), Stability, Approximations, and Inequalities, Dedicated to Professor Th.M. Rassias on the occasion of his 60th birthday, Springer Optimization and Its Applications 68(2012), 631–705 . DOI: https://doi.org/10.1007/978-1-4614-3498-6_39
A. Száz, Lower semicontinuity properties of relations in relator spaces, Adv. Stud. Contemp. Math. (Kyung-
shang) 23(2013), 107–158. DOI: https://doi.org/10.33589/23.5.0158
A. Száz, An extension of an additive selection theorem of Z. Gajda and R. Ger to vector relator spaces, Scientia, Ser A, Math. Sci. 24(2013), 33–54.
- NA
Similar Articles
- T. Roja Mary, K.P. Uma, A stochastic model for a single grade system with backup resource of manpower , Malaya Journal of Matematik: Vol. 2 No. 03 (2014): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2014 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.