Classes of Mappings in Metric Spaces

Authors

  • A.M. Ahmeda
  • Sid Ahmed Ould Ahmed Mahmoud

Keywords:

m-isometry, expansive map, contractive map, metric space

Abstract

The aim of this paper is to present certain basic properties of some class of mappings called (m,∞)-expansive and (m,∞)-contractive mappings acting on a real metric space. 

References

J. Agler, Hypercontractions and subnormality, J. Operator Theory 13 (1985) 203-217.

J. Agler and M. Stankus, m-Isometric transformations of Hilbert space I, Integral Equations and Operator Theory,21 (1995), 383-429.

A.M.A. Al Ahmadi, On the study of (m;¥)-isometric mappings on real metric spaces. Jouf University Science and Engineering Journal 2 (2019); 6(1): 1–13

A. Athavale, On completely hyperexpansive operators, Proc. Amer. Math. Soc. 124 (1996), 3745–3752.

F. Bayart, it m-isometries on Banach spaces, Math. Nachr. 284 (2011), 2141–2147.

T. Berm´udez, A. Martin´on and V. M¨uller, (m;q)-isometries on metric spaces, J. Operator Theory 72, No.2 (2014),313-329.

F. Botelho, On the existence of n-isometries on lp- spaces, Acta Sci. Math. (Szeged) 76 (2010), no. 1-2, 183–192.

B. P. Duggal, Tensor product of n-isometries III, Functional Analysis, Approximation and Computation 4:2(2012),61-67.

G. Exner , Il B. Jung , C. Li, k-hyperexpansive operators, J. Math. Anal. Appl. 323 (2006) 569-582.

C. Gu, On (m; p)-expansive and (m; p)-contractive operators on Hilbert and Banach spaces, J. Math. Anal. Appl. 426 (2015) 893-916.

C. Gu, The (m;q)-isometric weighted shifts on lp spaces, Integral Equations Operator Theory, 82(2015) 157–187.

P. Hoffman, M. Mackey and M. ´O Searc´oid, On the second parameter of an (m; p)-isometry, Integral Equat. Oper. Th.71(2011), 389-405.

S. Jung, Y. Kim, E. Ko and J. E. Lee (Seoul), On (A;m)-expansive operators, Studia Mathematica 213 (1) (2012).

A.Olofsson, An operator-valued Berezin transform and the class of n-hypercontractions, Integral Equations Operator Theory 58 (2007) 503–549.

F.Qi and B.N.Guo, Monotonicity of sequences involvung convex function and sequence, Math Inqual.Appl. Vol.9,No.2( 2006) 247–254.

O.A.M. Sid Ahmed, m-isometric operators on Banach spaces, Asian-European J. Math. 3(2010), 1-19.

O.A.M. Sid Ahmed, On A(m; p)-expansive and A(m; p)-hyperexpansive operators on Banach spaces-I, Al Jouf Sci. Eng. J. 1 (2014), 23-43.

[O.A.M. Sid Ahmed, On A(m; p)-expansive and A(m; p)-hyperexpansive operators on Banach spaces-II, J. Math. Comput. Sci. 5 (2015), No. 2, 123–148.

O.A.M. Sid Ahmed, On (m; p)-hyperexpansive mappings in Metric spaces, Note. Mat.35, no.2 (2015),17-37.

O. A. M. Sid Ahmed, On (m; p)-(hyper) expansive and (m; p)-(hyper) contractive mapings on a metric space, Journal of Inequalities and Special Functions,Volume 7 Issue 3(2016), Pages 73–87.

O. A. M. Sid Ahmed and Adel Saddi ,A-m- Isometric operators in Semi-Hilbertian spaces, Linear Algebra and its applications 436(10). 3929–3935 2010.

Sid Ahmed O. A. Mahmoud, Note on (A;m)- Isometric operators in semi-

Hilbertian, Journal of Innovative Science and Technology,(JIST) Issue(1) Vo.(1) 2019.

http://worldascience.com/journal/articles/July2019/JIST-1-1-2019-proceeding.pdf

V.M. Sholapurkar and A. Athavale, Completely and Alternatingly Hyperexpansive operators, J. Oper.Theory, 43(2000), 43-68.

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Published

2019-05-30

How to Cite

Ahmeda , A. ., & Ahmed Ould Ahmed Mahmoud, S. . (2019). Classes of Mappings in Metric Spaces. WAS Science Nature (WASSN) ISSN: 2766-7715, 2(1). Retrieved from http://worldascience.com/journals/index.php/wassn/article/view/7

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Section

Chemistry & Material Sciences