iosr-Jm   Volume-21 ~ Issue-6 ~ Nov. – Dec. 2025

Abstract : A linear transformation is a particular kind of mapping between linear spaces that respect the basic operations of vector addition and scalar multiplication. This study formulates a theoretical framework for studying linear transformations in the theory of fuzzy linear spaces over fuzzy fields. For this, the notion of μ-linear transformations a.....

Keywords: Fuzzy fields, fuzzy linear spaces, μ-linear transformations, isomorphisms of fuzzy linear spaces

[1] Gu Wenxiang and Lu Tu, Fuzzy Linear Spaces, Fuzzy Sets and Systems 49 (1992), 377- 380.
[2] Hoffman, K. and Kunze, R., Linear Algebra (2nd edition), Prentice-Hall, New Jersey, 1971.
[3] Klir, G.J. and Yuan, B., Fuzzy Sets and Fuzzy Logic : Theory and Applications, Prentice-Hall of India Private Limited, New Delhi, 2002.
[4] Kreyszig, E., 2005, Introductory Functional Analysis with Applications, John Wiley & Sons, New York.
[5] Lee, K.H., First Course on Fuzzy Theory and Applications, Springer Verlag, Heidelberg, 2005

Abstract : In this paper, the notions of fuzzy U-spaces and fuzzy ultranormal spaces are introduced and studied. Sufficient conditions for fuzzy strongly zero-dimensional spaces to become fuzzy U-spaces and fuzzy U-spaces to become fuzzy strongly zero-dimensional spaces are obtained. Certain fuzzy...

Keywords: Fuzzy 𝐹𝜎-set, fuzzy 𝐺𝛿-set, fuzzy clopen set, fuzzy simply* open set, fuzzy 𝐹′ space, fuzzy P-space, fuzzy perfectly disconnected space, fuzzy normal space, fuzzy connected space, fuzzy Brown space, fuzzy weakly 𝐹𝜎-complemented space, weak fuzzy Oz-space.
2020 AMS CLASSIFICATION : 54 A 40, 03 E 72.

[1]. N.Ajmal, J.K.Kohli, Zero dimensional and strongly zero dimensional fuzzy topological spaces, Fuzzy Sets and Systems, 61 (1994), 231 - 237.
[2]. F. Azarpanah and M. Karavan, On non regular ideals and z°-ideals in C(X), Czech. Math. J. 55 (130) ( June 2005), 397 – 407[1].
N.Ajmal, J.K.Kohli, Zero dimensional and strongly zero dimensional fuzzy topological spaces, Fuzzy Sets and Systems, 61 (1994), 231 - 237.
[2]. F. Azarpanah and M. Karavan, On non regular ideals and z°-ideals in C(X), Czech. Math. J. 55 (130) ( June 2005), 397 – 407

Abstract : Background: Influenza is an infectious viral disease of the upper respiratory tract caused by the orthomyxoviradae viruses, which occurs in subtypes A or B, depending on their core protein.The disease has always been a major issue of health concern in Nigeria and many parts of Africa and Asia with a yearly increase in the number of susceptible, infected and dead persons. Most mathematical models on the disease often employ the.....

Key Word: Informed class; Uninformed class;, Removed class; Brownian motion; Ito’s formula

[1] Alcaraz, GG., Vargas-De-Leon, C. Modeling control strategies for influenza A H1N1 epidemics: SIR models. Revista Mexicana de Fisica. 2012; 58(1): 37 – 43. Retrieved Sept. 7, 2025 from https://www.redalyc.orgarticulo.oa?id=5730391007.
[2] Bartlett, MS. Some evolutionary stochastic processes. Journal of Royal Statistical Society. 1949; B(11): 211 – 229.
[3] Cooper, BS, Pitman, RJ, Edmund, WJ and Gay, NJ. Delaying the international spread of pandemic influenza. PloS Medicin. 2006; 3(6):212. Retrieved Nov. 15, 2021, from http://www.journals .plos.org.
[4] Demir, E, Vural, C. An SIR model on influenza with the effects of treatment and vaccination. Journal of Mathematical Science and Modelling. 2024; 7(2): 51 – 59. Retrieved Sept. 7, 2025 from https://doi.org/10.33187/jmsm.1472066.
[5] Ferah, EM, Amine, S Ahmad, S, Nonlaopon, K, Allali, K. Theoretical and numerical results of stochastic models describing resistant and non-resistant strains of influenza. European Physical Journal Plus. 2020; 137.1169. Retrieved Jan. 10, 2023 from https://doi.org/10.1140/epjp/s13360-022-03302-5.

Abstract : This brief paper discusses the problem of long-term optimal consumption and investment. The corresponding model is formulated in terms of a discrete-time Markov control process. Rather than being concerned with the optimization of portfolio strategies, we are dealing with the accuracy of approximating the original control process with its deterministic version. In the case of small variances of returns on risky assets, we prove an inequality that gives an upper bound on the decrease in expected utility when implementing the approximation.

Key Word: Optimal investment and consumption policy; Markov control process; Deterministic approximation of a process; Upper bound of the stability index

[1]. Cruz-Suárez, H., Gordienko, E. and Montes-de-Oca, R. (2009) A note on deterministic approximation of discounted Markov decision processes. Applied Mathematics Letters, 22, 1252-1256.
[2]. Dynkin, R. M. and Yushkevich, A. A. (2012) Controlled Markov processes. Springer, New York.
[3]. Gordienko, E. I. (1992) An estimate of the stability of optimal control of certain stochastic and deterministic systems. J. Soviet Math., 59, 891-899.
[4]. Gordienko, E. I. and Yushkevich, A. A. (2003) Stability estimates in the problem of average optimal switching of a Markov chain. Math. Methods Oper. Res., 57, 345-365.
[5]. Hata, H. (2024) A long-term optimal consumption and investment problem with partial information. Mathematical Control and Related Fields, 14, 867-895.