Duality for Best Approximation in Fuzzy Quasi-normed Spaces

Singer, I.: Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Publishing House of the Academy of the Socialist Republic of Romania. Springer, New York (1970)

Eldred, A.A., Veeramani, P.: Existence and convergence of best proximity points. J. Math. Anal. Appl. 323(2), 1001–1006 (2006)

Shams, M., Vaezpour, S.M.: Best approximation on probabilistic normed spaces. Chaos Solitons Fract. 41(4), 1661–1667 (2009)

Goudarzi, M., Vaezpour, S.M.: Best simultaneous approximation in fuzzy normed spaces. Iran. J. Fuzzy Syst. 7(3), 87–96 (2010)

Hemati, F., Mazahri, H.: Exist and uniqueness of p-best approximation in fuzzy normed spaces (Poster). In: 46th Annual Iranian Mathematics Conference, pp. 25–28, August 2015. Yazd University

Lee, K.Y.: Approximation properties in fuzzy normed spaces. Fuzzy Sets Syst. 282, 115–130 (2016)

Vaezpour, S.M., Karimi, F.: t-Best approximation in fuzzy normed spaces. Iran. J. Fuzzy Syst. 5(2), 93–99 (2008)

Moghaddam, M.A.: Best proximity pairs in fuzzy normed spaces. J. Appl. Sci. 12(9), 893–896 (2012)

Mohsenialhosseini, S.A.M., Saheli, M.: Diameter approximate best proximity pair in fuzzy normed spaces. Sahand Commun. Math. Anal. 16(1), 17–34 (2019)

Moghaddam, M.A., Sistani, T.: On t-best coapproximation in fuzzy 2-normed spaces. Australian J. Basic Appl. Sci. 5(9), 2241–2248 (2011)

Reddy, B.S.: Some results on t-best approximation in fuzzy 2-normed linear spaces. Int. J. Pure Appl. Math. 72(2), 237–247 (2011)

Mohiuddine, S.A.: Some new results on approximation in fuzzy 2-normed spaces. Math. Comput. Model. 53, 574–580 (2011)

Kavikumar, J., Khamis, A., Manian, N.S.: t-Best approximation in intuitionistic fuzzy normed spaces. In: Proceedings: Conference Paper in IEEE International Conference on Fuzzy Systems, Barcelona, Spain, 18–23 July, 2010

Singer, I.: Duality for Nonconvex Approximation and Optimization. Springer, New York (2006)

Krein, M.G., Nudelman, A.A.: The Markov moment problem and extremum problems,” Nauka, Moscow 1973 (in Russian). English translation: Amer. Math. Society, Providence (1977)

Mustăţa, C.: On the extremal semi-Lipschitz functions. Rev. Anal. Numer. Theor. Approx. 31(1), 103–108 (2002)

Mustăţa, C.: On the uniqueness of the extension and unique best approximation in the dual of an asymmetric linear space. Rev. Anal. Numer. Theor. Approx. 32(2), 187–192 (2003)

Cobzas, S., Mustăţa, C.: Extension of bounded linear functionals and best approximation in spaces with asymmetric norm. Probat. J. 33(1), 191–212 (2004)

Cobzas, S.: Functional Analysis in Asymmetric Normed Spaces. Springer, Basel (2013)

Li, W. et al.: Best approximation in asymmetric normed linear spaces. In: International Conference on Information Science and Technology, March 26–28, 2011 Nanjing, Jiangsu, China

Gil, C.A.: Quasi-metric properties of the dual cone of an asymmetric normed space. Results Math. 77(4), 178 (2022)

Bachir, M., Flores, G.: Index of symmetry and topological classification of asymmetric normed spaces. Rocky Mountain J. Math. 50(6), 1951–1964 (2020)

Blasco, X., et al.: Computing optimal distances to Pareto sets of multi-objective optimization problems in asymmetric normed lattices. Acta Appl. Math. 159, 75–93 (2019)

Alegre, C., Romaguera, S.: Characterizations of metrizable topological vector spaces and their asymmetric generalizations in terms of fuzzy (quasi-)norms. Fuzzy Sets Syst. 61, 2181–2192 (2010)

Bag, T., Samanta, S.K.: Finite dimensional fuzzy normed linear spaces. Fuzzy Math. 6(2), 687–705 (2003)

Alegre, C., Romaguera, S.: On the uniform boundedness theorem in fuzzy quasi-normed spaces. Fuzzy Sets Syst. 282, 143–153 (2016)

Gao, R., Li, X.X., Wu, J.R.: The decomposition theorem for a fuzzy quasinorm. J. Math. 2020, Article ID 8845283, 7 (2020)

Li, R.N., Wu, J.R.: Hahn-Banach type theorems and the separation of convex sets for fuzzy quasi-normed spaces. AIMS Math. 7(3), 3290–3302 (2021)

Wang, H., Wu, J.R.: The norm of continuous linear operator between two fuzzy quasi-normed spaces. AIMS Mathematics 7(7), 11759–11771 (2022)

Alegre, C., Romaguera, S.: On paratopological vector spaces. Acta Math. Hungar. 101, 237–261 (2003)