Some Important Classes of the Continuous and Complex Interval-Valued Functions

Year 2023, , 46 - 55, 31.01.2023

Halise Levent , Yılmaz Yılmaz

https://doi.org/10.54974/fcmathsci.1158871

Abstract

This paper presents some important classes of the continuous functions defined from the set of real numbers to the space of complex intervals. These function spaces have an algebraic structure named as a quasilinear space which is suggested by Aseev in 1986. In this work, we analysis the quasilinear structure on the classes of the continuous and complex interval-valued functions. Further, we show that these spaces are the normed Ω-spaces. Finally, we examine the dimension of these function spaces.

Keywords

Normed quasilinear space, Complex interval, Continuous function, Dimension of a quasilinear space

References

• Alefeld G., Herzberger J., Einführung in die Intervallrechnung, Mannheim: Bibliographhisches Institut, 1974.
• Alefeld G., Herzberger J., Introduction to Interval Computations, Academic Press, 1983.
• Aseev S.M., Quasilinear operators and their application in the theory of multivalued mappings, Proceedings of the Steklov Institute of Mathematics, 2, 23-52, 1969.
• Aubin J.P., Frankowska H., Set-Valued Analysis, Birkhauser, 1990.
• Banazılı H.K., On Quasilinear Operators Between Quasilinear Spaces, M.Sc. Thesis, İnönü University, Malatya, Türkiye, 2014.
• Bozkurt H., Yılmaz Y., Some new results on inner product quasilinear spaces, Cogents Mathematics, 3(1), 1-10, 2016.
• Crouzet J.F., Strauss O., Interval-valued probability density estimation based on quasi-continuous histograms: Proof of the conjecture, Fuzzy Sets and Systems, 183, 92-100, 2010.
• Graba G., Strauss O., An interval-valued inversion of the non-additive interval-valued F-transform: Use for upsampling a signal, Fuzzy Sets and Systems, 288, 26-45, 2016.
• Jaulin L., Kieffer M., Didrit O., Walter E., Applied Interval Analysis with Examples in Parameter and State Estimation, Robust Control and Robotics, Springer-Verlag, 2001.
• Kulisch U., Grundzüge der Intervallrechnung, Jahrburch Überblicke Mathematik, Mannheim: Bibliographhisches Institut, 1969.
• Levent H., Yılmaz Y., An application: Representations of some systems on non-deterministic EEG signals, Journal of Biostatistics and Biometric Applications, 3(1), 101, 2017.
• Levent H., Yılmaz Y., Translation, modulation and dilation systems in set-valued signal processing, Carpathian Mathematical Publications, 10, 10-31, 2018.
• Moore R.E., Kearfott R.B., Cloud M.J., Introduction to Interval Analysis, SIAM, 2009.
• Rico A., Strauss O., Imprecise expactations for imprecise linear filtering, International Journal of Approximate Reasoning, 51(8), 933-947, 2008.
• Yılmaz Y., Levent H., Inner-product quasilinear spaces with applications in signal processing, Advanced Studies: Euro-Tbilisi Mathematical Journal, 14(4), 125-146, 2021.
• Yılmaz Y., Bozkurt H., Çakan S., On orthonormal sets in inner product quasilinear spaces, Creative Mathematics and Informatics, 25(2), 237-247, 2016.