Soft Quasilinear Operators

Year 2022, Volume: 10 Issue: 2, 82 - 92, 01.06.2022

Hacer Bozkurt

Abstract

In this paper, we have introduced a concept of soft quasilinear operator over soft quasilinear spaces which extends the notion of quasilinear operator. Also, we studied some properties of soft quasilinear operators with illustrating examples. Further, we have defined inverse of a soft quasilinear operator and its some different properties from inverse of soft linear operators are obtained.

Keywords

Quasilinear space , Soft quasilinear space , Nomred quasilinear space , Soft normed quasilinear space

Supporting Institution

Batman University

References

• [1] Aseev, S. M.: Quasilinear operators and their application in the theory of multivalued mappings. Proceeding of the Steklov Instiute of Mathematics. 2, 23-52 (1986).
• [2] Çakan, S. and Yılmaz, Y.: Normed Proper Quasilinear Spaces. Journal of Nonlinear Sciences and Applications. 8, 816-836 (2015).
• [3] Rojas-Medar, M. A., Jiménez-Gamerob, M. D., Chalco-Canoa, Y. and Viera-Brandão, A. J.: Fuzzy quasilinear spaces and applications. Fuzzy Sets and Systems. 152, 173-190 (2005).
• [4] Levent, H. and Yılmaz, Y.: Translation, modulation and dilation systems set-valued signal processing. Carpathian Mathematical Publications. 10, No.1, 143-164 (2018).
• [5] Bozkurt, H. and Yılmaz, Y.: Some New Properties of Inner Product Quasilinear Spaces. Bulletin of Mathematical Analysis and Applications. 8, No.1, 37-45(2016).
• [6] Bozkurt, H. and Yılmaz, Y.: On Inner Product Quasilinear Spaces and Hilbert Quasilinear Spaces. Information Sciences and Computing. vol.2016, Article ID ISC671116, 12 pp.(2016).
• [7] Bozkurt, H. and Yılmaz, Y.: Some New Results on Inner Product Quasilinear Spaces. Cogent Mathematics. 3 1194801, 10 pp. (2016).
• [8] Bozkurt, H. and Yılmaz, Y.: New Inner Product Quasilinear Spaces on Interval Numbers. Journal of Function Spaces. vol. 2016, Article ID 2619271, 9 pp.(2016).
• [9] Yılmaz, Y., Bozkurt, H. and Çakan, S.: An orthonormal sets in inner product quasilinear spaces. Creative Mathematics and Informatics. 25, No.2 237-247 (2016).
• [10] Levent, H. and Yılmaz, Y.: Hahn- Banach extension theorem for interval-valued functions and existence of quasilinear functionals. New Trends in Mathematical Sciences. NTMSCI 6 No.2, 19-28 (2018).
• [11] Molodtsov, D.: Soft set theory first results. Comput. Math. Appl. 37, 19-31 (1999).
• [12] Maji, P. K., Biswas, R. and Roy, A. R.: An application of soft sets in a decision making problem. Comput. Math. Appl. 44, 1077-1083 (2002).
• [13] Maji, P. K., Biswas, R. and Roy, A. R.: Soft set theory. Comput. Mat. Appl. 45, 555-562 (2003).
• [14] Shabir, M. and Naz, M.: On soft topological spaces. Comput. Math. Appl. 61, 1786-1799 (2011).
• [15] Akta¸s, H. and Ça ˘gman, N.: Soft sets and soft groups. Inform. Sci. 177, 2226-2735 (2007).
• [16] Sezgin, A. and Atagün, A. O.: A new kind o vector space: soft vector space. Southeast Asian Bulletin of Mathematics, 40(5), 753-770.
• [17] Das , S. and Samanta, S. K.: Soft linear operators in soft normed linear spaces. Annals of Fuzzy Mathematics and ˙Informatics. Vol. 6, No.2 295-314 (2013).
• [18] Das , S. and Samanta, S. K.: On soft metric spaces. J. Fuzzy Math. Vol.21, No.3 707-734 (2013).
• [19] Das , S. and Samanta, S. K.: On soft inner product spaces. Ann. Fuzzy Math. Inform. 6(1), 151-170 (2013).
• [20] Bozkurt, H.: Soft quasilinear spaces and soft normed quasilinear spaces. Adıyaman University Journal of Science. 10(2), 506-523 (2020).