Volume 19, Issue 2 (9-2024)
IJMSI 2024, 19(2): 119-126 |
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Garg S, Grover H K, Narang T D. Rotundity of Quotient Spaces in Metric Linear Spaces. IJMSI 2024; 19 (2) :119-126
URL: http://ijmsi.ir/article-1-1776-en.html
URL: http://ijmsi.ir/article-1-1776-en.html
Abstract:
In this paper, we discuss the inheritance of strict convexity, uniform convexity and local uniform convexity by the quotient spaces of metric linear spaces. We also show that, as in the case of normed linear spaces, completeness is a three- space property in metric linear spaces as well.
Keywords: Metric linear space, Strict convexity, Uniform convexity, Local uniform convexity, Three-space property.
Type of Study: Research paper |
Subject:
Special
References
1. G. C. Ahuja, T. D. Narang, S. Trehan, An Approximation Problem in Metric Linear Spaces, Math. Student, 40, (1972), 447-448.
2. G. C. Ahuja, T. D. Narang, S. Trehan, Best Approximation on Convex Sets in Metric Linear Spaces, Math. Nachr., 78(1), (1977), 125-130. [DOI:10.1002/mana.19770780110]
3. Naum I. Akhiezer, Mark G. Krein, Some Questions in The Theory of Moments, Translations of Mathematical Monographs, AMS, Providence, 2, 1962.
4. G. Albinus, Normaritge Metriken auf Metrisierbaren Lokalkovexen Topologischen Vektor¨ aumen, Math. Nachr., 37, (1968), 177-196. [DOI:10.1002/mana.19680370305]
5. A. R. Alimov, I. G. Tsar'kov, Approximatively Compact Sets in Asymmetric EfimovSteckin Spaces and Convexity of Almost Suns, Math. Notes, 110(6), (2021), 947-951. [DOI:10.1134/S0001434621110316]
6. James A. Clarkson, Uniformly Convex Spaces, Trans. Amer. Math. Soc., 40(3), (1936), 396-414. [DOI:10.1090/S0002-9947-1936-1501880-4]
7. Shelly Garg, Harpreet K. Grover, T. D. Narang, Different Forms of Convexity in Metric Linear Spaces, Electronic Journal of Mathematical Analysis and Applications, to appear.
8. Victor L. Klee, Some New Results on Smoothness and Rotundity in Normed Linear Spaces, Math. Ann., 139, (1959), 51-63. [DOI:10.1007/BF01459822]
9. A. R. Lovaglia, Locally Uniformly Convex Banach Spaces, Trans. Amer. Math. Soc., 78(1), (1955), 225-238. [DOI:10.1090/S0002-9947-1955-0066558-7]
10. Robert E. Megginson, An Introduction to Banach Space Theory, Springer-Verlag, 1998. [DOI:10.1007/978-1-4612-0603-3]
11. T. D. Narang, Different Types of Convexities in Metric Linear Spaces, Jnanabha, 7, (1977), 17-20.
12. Stefan Rolewicz, Metric Linear Spaces, Mathematics and Applications, D. Reidel Publishing Company, 1985.
13. Walter Rudin, Functional Analysis, Tata McGraw- Hill Publishing Company Ltd., 1974.
14. K. P. R. Sastry, S. V. R. Naidu, Convexity Conditions in Metric Linear Spaces, Mathematics Seminar Notes, 7, (1979), 235-251.
15. K. P. R. Sastry, S. V. R. Naidu, Uniform Convexity and Strict Convexity in Metric Linear Spaces, Math. Nachr., 104, (1981), 331-347. [DOI:10.1002/mana.19811040124]
16. I. G. Tsar'kov, Uniform Convexity in Nonsymmetric Spaces, Math. Notes, 110(5), (2021), 773-783. [DOI:10.1134/S0001434621110146]
17. A. I. Vasil'ev, Chebyshev Sets and Strong Convexity of Metric Linear Spaces, Math.Notes, 25, (1979), 335-340. [DOI:10.1007/BF01224836]
18. A. I. Vasil'ev, Approximative Compactness in Linear Metric Spaces, Math. Nachr., 160, (1993), 329-341.
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