Aralık Değerli Cesaro Yakınsak Diziler Uzayı Üzerine

Yıl 2023, Cilt: 13 Sayı: 1&2, 1 - 17, 31.12.2023

Gülsen Kılınç , Mehmet Sezai Yıldırım

https://doi.org/10.37094/adyujsci.1296930

Öz

Quasilineer uzay kavramı, temelleri S. M. Aseev'in 1986 yılında yayınlanan çalışmasıyla atılan, olgunlaşması gereken bir alandır. Lineer olmayan Quasilineer uzayın en basit örneği, gerçek sayıların kapalı aralıklar sınıfı olan 𝑃 kümesidir. Bu çalışmada Cesàro limitleme yönteminin matris etki alanı kullanılarak aralık değerli bir dizi uzayı verildi. Ayrıca bu uzayın quasilineer uzay yapısı, bazı topolojik özellikleri ve bazı kapsama ilişkileri incelendi.

Anahtar Kelimeler

Quasilineer Uzay, Aralık Değerli Dizi, Hausdorff Metrik, Cesàro yakınsaklık

On the Interval Valued Cesaro Convergent Sequences Space

Öz

The concept of quasilinear space is a field that needs to be matured, the foundations of which were laid by S. M. Aseev's published work in 1986. The simplest nonlinear quasi linear space example is the set 𝑃 which is a class of closed intervals of real numbers. In this study, it was given an interval-valued sequence space using the Cesàro limitation method's matrix domain. Also, its quasilinear space structure, some topological characteristics, and some inclusion relations were examined.

Anahtar Kelimeler

Quasilinear Space, Interval Valued Sequence, Hausdorff Metric, Cesàro Convergence.

Kaynakça

• Zadeh, L.A., Fuzzy sets, Information and Control 8, 338–353, 1965.
• Dwyer, P.S., Linear computations, New York, Wiley, 1951.
• Moore, R.E., Automatic error analysis in digital computation, Lockheed Missiles and Space Co. Technical Report LMSD-48421, Palo Alto, CA, 1959.
• Moore, R.E. and Yang, C.T., Interval analysis I, LMSD285875, Lockheed Missiles and Space Company, 1962.
• Moore, R.E., Kearfott, R.B. and Cloud, M.J., Introduction to interval analysis, Society for Industrial and Applied Mathematics, Philadelphia, 2009.
• Nanda, S., On sequences of fuzzy numbers, Fuzzy Sets and Systems 33, 123–126, 1989.
• Talo, Ö. and Başar, F., Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations, Computers and Mathematics with Applications 58, 717–733, 2009.
• Altın, Y., Mursaleen, M. and Altınok, H., Statistical summability (C,1) for sequences of fuzzy real numbers and a Tauberian theorem, Journal of Intelligent & Fuzzy Systems 21 (6), 379–384, 2010.
• Altınok, H., Çolak, R. and Altın, Y., On the class of λ-statistically convergent difference sequences of fuzzy numbers, Soft Computing 16 (6), 1029–1034, 2012.
• Altınok, H., Çolak, R. and Et, M., λ−difference sequence spaces of fuzzy numbers, Fuzzy sets and Systems 160, 3128–3139, 2009.
• Hong, D.H. and Lee, S., Some algebraic properties and a distance measure for interval-valued fuzzy numbers, Information Sciences 148, 1-10, 2002.
• Şengönül, M. and Eryılmaz, A., On the sequence spaces of interval numbers, Thai Journal of Mathematics, 8(3), 503-510, 2010.
• Aseev, S.M., Quasilinear operators and their application in the theory of multivalued mappings, Proc. Steklov Inst. Math., 167, 23–52, 1986.
• Alefeld, G. and Mayer, G., Interval analysis: Theory and applications, J. Comput. Appl. Math., 121, 421–464, 2000.
• Lakshmikantham, V., Gnana Bhaskar, T. and Vasundhara Devi, J., Theory of set differential equations in metric spaces, Cambridge Scientific Publishers, Cambridge, 2006.
• Rojas-Medar, M.A., Jiménez-Gamero, M.D., Chalco-Cano, Y., & Viera-Brandão, A.J., Fuzzy quasilinear spaces and applications, Fuzzy Sets and Systems, 152, 173 –190, 2005.
• Yılmaz, Y., Bozkurt, H., Çakan, S., On orthonormal sets in inner product quasilinear spaces, Creat. Math. Inform. 25 (2), 237-247, 2016.
• Yılmaz, Y., Bozkurt, H., Levent, H., Çetinkaya, Ü., Inner product fuzzy quasilinear spaces and some fuzzy sequence spaces, Journal of Mathematics, No.2466817, 1-15, 2022.
• Kreyszig, E., Introductory functional analysis with applications, John Wiley & Sons. Inc., 1978.
• Şengönül, M., On the Zweier sequence spaces of fuzzy numbers, International Journal of Mathematics and Mathematical Sciences, 2014, Article ID 439169, 1-9, 2014.
• Şengönül, M., Başar, F., Some new Cesàro sequence spaces of non-absolute type which include the spaces and , Soochow J. Math. 31 (1), 107-119, 2005.
• Zararsız, Z., Şengönül, M., The Application Domain of Cesàro Matrix on Some Sequence Spaces of Fuzzy Numbers, International Journal of Mathematical Analysis, 9 (1), 1–14, 2015.
• Chiao, K., Fundamental properties of interval vector max-norm, Tamsui Oxford J. Math. Sci., 18 (2), 219-233, 2002.
• Yılmaz, Y., Bozkurt, H, Levent, H., Çetinkaya, Ü., Inner product fuzzy quasilinear spaces and some fuzzy sequence spaces, Journal of Mathematics, 2022, Article ID 2466817, 1-15, 2022.
• Bozkurt, H., Yılmaz, Y., New inner products quasilinear spaces on interval numbers, Journal of Function Spaces, 2016, Article ID:2619271, 1-9, 2016.
• Levent, H., Yılmaz, Y., Inner-product quasilinear spaces with applications in signal processing, Euro-Tbilisi Mathematical Journal, 14, (4), 25-146, 2021.
• Levent, H., Yılmaz, Y., Translation, modulation and dilation systems in set-valued signal processing, Carpathian Math. Publ. 10, (1), 143-164, 2018.
• Bozkurt, H., Yılmaz, Y., Some new results on inner product quasilinear spaces, Cogent Mathematics, 3, 1194801, 2016.
• Levent, H., Yılmaz, Y., Analysis of signals with inexact data by using interval-valued functions, The Journal of Analysis, 30 (4), 1635-1651, 2022.
• Levent, H., Yılmaz, Y., Bozkurt, H., On the inner-product spaces of complex interval sequences, Communication in Advanced Mathematical Sciences, 5,4, 180-188, 2022.
• Levent, H., Yılmaz, Y., Fourier transform of interval sequences and its applications, Journal of Intelligent & Fuzzy Systems, (Accepted) 2023.