Felbin C Kennedy

Clementina Felbin: “Finite dimensional fuzzy normed linear space”, Fuzzy sets and systems 48 (1992) 239 – 248, North – Holland. This paper contributes to fundamental work in the area of fuzzy normed linear space and there are works based on fuzzy normed linear space of the Felbin’s type. This paper currently has 601 citations.

​

Osmo Kaleva, in his paper titled “A comment on the completion of fuzzy metric spaces” (Fuzzy Sets and Systems, 2008), cited that my work is fundamental. Tarapada Bag & Syamal Kumar Samanta, in their paper titled “A comparative study of fuzzy norms on a linear space” (Fuzzy sets and systems, 2008), classified my work to be “fuzzy normed linear space of the Felbin’s Type”. Following this, several papers began to use the same terminology, even titling their works to be in the area of 'the Felbin's type'. Few of those works have been mentioned here.

​

1. T. Bag and S K Samantha, “Fuzzy bounded linear operators in Felbin's type fuzzy normed linear spaces”, Fuzzy Sets and Systems 159 (6) : 685 -707, 2008.

2. T. Bag, “Some Fundamental Theorems in Felbin’s Type Fuzzy Normed Linear Spaces”, International Journal of Mathematics and Scientific Computing, 1 (2): 44-49, 2011.

3. Mohammad Janfada, Abolfazl Nezhadali Baghan, “ On Felbin’s-Type Fuzzy 2-Normed Linear Spaces and its I-topologies”, Fuzzy Systems and Mathematics, 26 (1): 1-12, 2012.

4. Fridoun Moradlou, Saber Rezaee and Ildar Sadeqi, “Approximate Quadratic Functional Equation in Felbin’s Type Normed Linear Spaces”, Hacettepe Journal of Mathematics and Statistics Volume 42 (5) : 501 – 516, 2013.

5. I. Sadeqi, F. Moradlou and M. Salehi, “On Approximate Cauchy Equation in Felbin’s Type Fuzzy Normed Linear Spaces”, Iranian Journal of Fuzzy Systems 10 (3) : 51-63, 2013.

6. Bag, T. and Samanta, S. K, Fuzzy Reflexivity of Felbin's Type Fuzzy Normed Linear Spaces and Fixed Point Theorems in Such Spaces, Iranian Journal of Fuzzy Systems 8 (5) : 103 -115, 2013.

7. John M. Rassias, Matina J. Rassias, M. Arunkumar and T. Namachivayam, “Ulam-Hyers stability of a 2-variable AC-mixed type functional equation in Felbin's type spaces”: fixed point method, International Mathematical Forum, 8 (25 – 28): 1307 – 1322, 2013

8. Ashraf Zohourmeskar, “Compact Operators in Felbins Type Fuzzy Normed Linear Spaces”, Journal of Mathematics and Computer Science (JCMS), 10 (3): 199-202, 2014.

9. G. Z. Eskandani & J. M. Rassias ,“Approximation of a General Cubic Functional Equation in Felbin’s Type Fuzzy Normed Linear Spaces” Results in Mathematics 66:113–123, 2014.

10. S Murthy, M Arunkumar, G Ganapathy, “Solution and Stability of n-Dimensional Cubic Functional Equation in Felbins Type Spaces: Direct and Fixed Point Methods”, International Conference on Mathematical Sciences, Elsevier Publication : 81 - 88, 2014.

11. K. Ravi, J.M.Rassias, Sandra Pinelas and P.Narasimman, “The Stability of a Generalized Radical Reciprocal Quadratic Functional Equation in Felbin’s Space”, PanAmerican Mathematical Journal 24 (1): 75–92, 2014.

12. Reza Chaharpashlou, Ashraf Zohourmeskar, “The equality in Felbin’s type fuzzy normed linear spaces”, International Research Journal of Applied and Basic Sciences  www.irjabs.com ISSN 2251-838X/ Vol, 8 (9): 1240-1242 Science Explorer Publications, 2014.

13. A.Zohourmeskar, A.Mozaffarikhan, “Arzela-Ascoli theorem for Felbin’s type fuzzy normed linear spaces”, Journal of mathematics and computer science  13: 90-93, 2014

14. K Ravi, S Sabarinathan, “A Quadratic Functional Equation and its Stability in Felbin's Type Spaces”, Far East Journal of Mathematical Sciences, 98 (8) : 977 - 998, 2015

15. Wenping Xue, Peisheng Ji, “On the stability of Jensen functional equation in Felbin’s type fuzzy normed linear spaces” Proceedings of the 3rd International Conference on Mechatronics, Robotics and Automation (2015),  https://doi.org/10.2991/icmra-15.2015.110

16. Pasupathi Narasimman, John M. Rassias and Krishnan Ravi, “n-dimensional quintic and sextic functional equations and their stabilities in Felbin type spaces”, Georgian Math. J. 23 (1):121-137, 2016: https://doi.org/10.1515/gmj-2015-0039

17. Mami Sharma and Debajit Hazarika, “On linear operators in Felbin’s fuzzy normed linear space”, Annals of Fuzzy Mathematics and Informatics  13 (6): 749–758, 2017.

18. CHANG Xiao-xuan, JI Pei-sheng, “Class of fuzzy bounded operators in Felbin’s type fuzzy normed linear spaces”, Journal of Shandong University(Natural Science), 52 (2): 49-54, 2017.

19. S. Murthy, M. Maria Susai Manuel, M. Arunkumar and G. Ganapathy, “Quartic Functional Equation Involving Sum of Functions of Consecutive Variables is Stable in Felbin's Type Cone Normed Spaces”, Malaya J. Mat. 5(1): 29–40, 2017.

20. M. Arunkumar, S. Karthikeyan and S. Ramamoorthi, Stability of n-dimensional Quartic Functional Equation in Felbin’s Spaces: Direct and Fixed point methods”, Malaya Journal of Matematik , 5 (1) : 58-71, 2017. 

21. Wang, Zhihua, “Stability of a more general cubic functional equation in Felbin’s type fuzzy normed linear spaces”,  Journal of Intelligent & Fuzzy Systems, 38 (4): 4733-4742, 2020

22. Ju Myung Kim and Keun Young Lee, “A Study of Approximation Properties in Felbin-Fuzzy Normed Spaces”, Mathematics, 8(2), 2020. https://doi.org/10.3390/math8020161

23. John Michael Rassias, Narasimman Pasupathi, Reza Saadati, and Manuel de la Sen, “Approximation of Mixed Euler-Lagrange -Cubic-Quartic Functional Equation in Felbin’s Type f-NLS” Hindawi : Journal of Function Spaces / 2021/ Volume 2021 | Article ID 8068673 / https://doi.org/10.1155/2021/8068673