Manaf Adnan Saleh Saleh1, Aamena Al-Qabani2, and Amar Bougoutaia3
1Department of Mathematics and Computer Applications, College of Sciences, Al-Nahrain University, Baghdad, Iraq
2Department of Mathematics and Computer Applications, College of Sciences, Al-Nahrain University, Baghdad, Iraq
3Laboratory of Pure and Applied Mathematics (LPAM), University of Laghouat, Algeria
Received: November 17, 2023 Accepted: February 12, 2024 Publication Date: March 23, 2024
Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.
Building upon the interpolative classical results of D. Achour, P. Rueda, and R. Yahi for Lipschitz ideals we define the interpolative fuzzy Lipschitz ideal concept for fuzzy Lipschitz operators between fuzzy metric spaces and complete fuzzy normed spaces which is a natural generalization of the notion of absolutely (crisp) Lipschitz (p, θ)-summing maps. The fuzzy Lipschitz norm of the aforementioned notion is defined and prove its fuzzy Lipschitz norm is a fuzzy real number. Afterwards we establish a fundamental characterizations of absolutely interpolative fuzzy Lipschitz (p, θ)-summing map. This is over by establishing a fuzzy version of nonlinear Pietsch Domination Theorem. Finally, we raise some open problems which we think are interesting.
Keywords: Lipschitz ideals; Fuzzy functional analysis; Fuzzy real analysis
[1] J.-Z. Xiao and X. Zhu, (2002) “On linearly topological structure and property of fuzzy normed linear space" Fuzzy Sets and Systems 125: 153–161. DOI: 10.1016/ S0165-0114(00)00136-6.
[3] M. A. S. Saleh, (2021) “Interpolative Lipschitz ideals" Colloquium Mathematicum 163: 153–170. DOI: 10.4064/cm7844-10-2019.
[4] J. Farmer and W. Johnson, (2009) “Lipschitz psumming operators" Proceedings of the American Mathematical Society 137: DOI: 10.1090/S0002-9939- 09-09865-7.
[5] D. Achour, E. Dahia, and M. A. S. Saleh, (2018) “Multilinear mixing operators and Lipschitz mixing operator ideals" Oper. Matrices 12(4): 903–931.
[6] D. Achour, P. Rueda, and R. Yahi, (2017) “(p, σ)- Absolutely Lipschitz operators" Annals of Functional Analysis 8(1): 38–50. DOI: 10.1215/20088752-3720614.
[7] B. Daraby and J. Jafari, (2016) “Some properties of fuzzy real numbers" Sahand Communications in Mathematical Analysis 03(1): 21–27.
[8] M. A. S. Saleh, (2017) “New types of Lipschitz summing maps between metric spaces: New types of Lipschitz summing maps between metric spaces" Mathematische Nachrichten 290: 1347–1373. DOI: 10.1002/mana.201500020.
[9] M. A. S. Saleh, (2021) “Computations of Lipschitz Summing Norms and Applications" Colloquium Mathematicum 165: 31–40. DOI: 10.4064/6-3-2020.
[10] M. A. S. Saleh, R. Ahmood, and L. Khaleel, (2022) “Fuzzy Operator Ideals" Journal of Engineering and Applied Science 26: 339–346. DOI: 10.6180/jase.202303_26(3).0005.
[11] A. Hasankhani, A. Nazari, and M. Saheli, (2010) “Some properties of fuzzy Hilbert spaces and norm of operators" Iranian Journal of Fuzzy Systems 7:
We use cookies on this website to personalize content to improve your user experience and analyze our traffic. By using this site you agree to its use of cookies.
