Fuzzy Fonksiyon Dönüşüm Dizilerinin μ. Dereceden Kuvvetli p-Lacunary İstatistiksel Yakınsaklığı
Yıl 2021,
Sayı: 31, 823 - 830, 31.12.2021
Abdulkadir Karakaş
Hakkan Güloğlu
Öz
Bu çalışmada, fuzzy küme, fuzzy dizileri ve fuzzy sayı dizilerinin yakınsaklığı ve istatistiksel yakınsaklığı gibi bilinen kavramlar incelenerek, literatürde bilinen fuzzy fonksiyon dizilerinin tanımı ve dizilerin noktasal yakınsaklığı kavramı kullanılarak, fuzzy fonksiyon dizilerinin μ. dereceden kuvvetli p-lacunary istatistiksel yakınsaklık ile fuzzy fonksiyon dizilerinin μ. dereceden lacunary istatistiksel yakınsaklık kavramları tanımlanarak S_Φ^μ (f),N_Φ^μ (f) ve N_(Φ,p)^μ (f) uzayları arasında bazı kapsama bağıntıları ile ilgili sonuçlar elde edilerek bunlar arasındaki ilişkiler incelenmiştir.
Kaynakça
- Zadeh, L.A. (1965). Fuzzy sets, Inform and Control, 8, ss. 338-353.
- Matloka, M. (1986) .Sequences of fuzzy numbers, Busefal, 28, ss. 28-37.
- Nanda, S. (1989). On sequence of fuzzy numbers, Fuzzy Sets and Systems,33, ss. 123-126.
- Nuray, F. and Savaş, E. (1995). Statistical convergence of fuzzy numbers, Mathematica Slovaca, 45 (3), ss. 269-273.
- Subrahmanyam, P.V. (1999). Cesàro summability for fuzzy real numbers, The Journal of Analysis, 7, ss. 159-168.
- Kwon, J.S. (2000). On statistical and Cesàro convergence of fuzzy numbers, Korean Journal of Computational.&Appllied Mathematics, 7 (1), ss. 195-203.
- Aytar S.and Pehlivan, S. (2007) Statistical cluster and extreme limit points of sequences of fuzzy numbers, Information Sciences, 177, 3290--3296.
- Altin, Y., Et, M.and Çolak, R. (2006). Lacunary statistical and lacunary strongly convergence of generalized difference sequences of fuzzy numbers, Computers & Mathematics with Applications, 52 (6-7), ss1011-1020.
- Karakaş, A., Altin, Y. and Altinok, H. (2014). On generalized statistical convergence of order β-of sequences of fuzzy numbers, Journa of Intelligent &. Fuzzy Systems, 26 (4), ss. 1909-1917.
- Zygmund, A. (1968). Trigonometric series: Vols. I, II. Cambridge University Press, London-New York.
- Steinhaus, H. (1951). Surla convergence ordinarie et la convergence asymptotique, Colloquium Mathematicum, 2, ss. 73-74.
- Fast, H. (1951). Sur la convergence statistique, Colloquium Mathematicum, 2, ss. 241-244.
- Fridy, J.A. (1985). On the statistical convergence, Analysis, 5, ss. 301-313.
- Šalát, T. (1980). On statistically convergent sequences of real numbers. Mathematica Slovaca, 30 (2), ss. 139-150.
- Connor, J.S (1988). The statistical and strong p-Cesàro convergence of sequences, Analysis, 8 (1-2), ss. 47-63.
- Tripathy, B.C. and Sen, M. (2001). On generalized statistically convergent sequences, Indian Journal of Pure Applied Mathematics, 32 (11), ss.1689-1694.
- Gadjiev, A. D. and Orhan, C.(2002). Some approximation theorems via statistical convergence, Rocky Mountain Journal of Mathematics, 32 (1), ss. 129-138.
- Çolak, R. (2010). Statistical convergence of order α, Modern Methods in Analysis and Its Applications, Anamaya Pub., New Delhi, India, ss. 121-138.
- Freedman, A.R., Sember, J.J. and Raphael, M. (1978). "Some Cesaro-type summability spaces", Proc. Lond. Math. Soc., 37, 508-520.
- Fridy, J. A. and Orhan, C. (1993). Lacunary Statistical Convergence, Pacific J. Math. 160 (1) 43-51.
- Duman, O. and Orhan, C. (2004). μ-statistically convergent function sequences, Czechoslovak Mathematical Journal. 54 (129) no. 2, ss. 413-422.
- Gökhan, A. and Güngör, M. (2002). On pointwise statistical convergence, Indian Journal of Pure Applied Mathematics, 33 (9), ss. 1379-1384.
- Çinar, M.; Karakaş, M., Et, M. (2013). On pointwise and uniform statistical convergence of order α for sequences of functions, Fixed Point Theory and Application, 33, 11 pp.
- Nuray, F., (1998). Lacunary statistical convergence of sequences of Fuzzy numbers, Fuzzy Sets Syst., 99 353-355.
- Şengül, H. and Et, M. (2014). On lacunary statistical convergence of order α, Acta Math. Sci. Ser. B Engl. Ed. 34 (2), 473-482.
- Bhardwaj, V. K. and Dhawan, S. (2016). Density by moduli and lacunary statistical convergence, Abstr. Appl. Anal., Art. ID 9365037, 11 pp.
- Das, G., and Mishra, S.K. (1983). Banach limits and lacunary strong almost convegence, J.Orissa Math. Soc.2, 61-70.
- Puri, M. L. and Ralescu, D.A. (1986). Fuzzy random variables, Journal of Mathematical Analysis and Applications, 114, ss. 409-422.
- Mursaleen, M. and Başarır, M. (2003). On some new sequence spaces of fuzzy numbers, Indian Journal of Pure and Applied Mathematics, 34 (9), ss.1351-1357.
- Matloka, M. (1987). Fuzzy mappings- sequences and series, Busefal, 30, ss.18-25.
- Altin, Y. Et, M. ve Tripathy, B. C. (2007). On pointwise statistical convergence of sequences of fuzzy mappings, Journal Fuzzy Mathematics, 15 (2), ss. 425-433.
- Et, M., Tripathy, B.C. ve Dutta, A.J. (2014). On pointwise statistical convergence of order α-of sequences of fuzzy mappings, Kuwait Journal of Science, 41 (3), ss. 17-30.
- Et, M. (2014). On pointwise λ-statistical convergence of order α-of sequences of fuzzy mappings, Filomat, 28 (6), ss.1271-1279.
- Gong, Z., Zhang, L.ve Zhu, X. (2015). The statistical convergence for sequences of fuzzy-number-valued functions, Information Sciences, 295, ss. 182-195.
- Srivastava, P.D. ve Ojha, S. (2014). λ-Statistical convergence of fuzzy numbers and fuzzy functions of order θ, Soft Computing, 18,ss. 1027-1032.
- Hung, N. V., Tam, V. M., Tuan, N. H.and O'Regan, D. (2020). Convergence analysis of solution sets for fuzzy optimization problems, Journal of Computational and Applied Mathematics, 369, 112615, 11 pp.
- Hazarika, B. (2017). Pointwise ideal convergence and Uniformly ideal convergence of sequence of fuzzy valued functions, Journal of İntelligent & Fuzzy Systems, 32 (3), ss. 2665-2677.
μ. Order Strong p-Lacunary Statistical Convergence of Fuzzy Function Mapping Sequences
Yıl 2021,
Sayı: 31, 823 - 830, 31.12.2021
Abdulkadir Karakaş
Hakkan Güloğlu
Öz
In this paper, we investigate the known concepts such as fuzzy set, fuzzy sequences and convergence and statistical convergence of fuzzy number sequences. Additionally, we define μ. order strong p-lacunary statistical convergence and μ. order the lacunary statistical convergence of the order of squences of fuzzy functions by using the definition of fuzzy function sequences and the concept of point convergence of sequences known in the literature. Then, we investigate the results about some coverage relations between the S_Φ^μ (f),N_Φ^μ (f) and N_(Φ,p)^μ (f) spaces and we present the relations between.
Kaynakça
- Zadeh, L.A. (1965). Fuzzy sets, Inform and Control, 8, ss. 338-353.
- Matloka, M. (1986) .Sequences of fuzzy numbers, Busefal, 28, ss. 28-37.
- Nanda, S. (1989). On sequence of fuzzy numbers, Fuzzy Sets and Systems,33, ss. 123-126.
- Nuray, F. and Savaş, E. (1995). Statistical convergence of fuzzy numbers, Mathematica Slovaca, 45 (3), ss. 269-273.
- Subrahmanyam, P.V. (1999). Cesàro summability for fuzzy real numbers, The Journal of Analysis, 7, ss. 159-168.
- Kwon, J.S. (2000). On statistical and Cesàro convergence of fuzzy numbers, Korean Journal of Computational.&Appllied Mathematics, 7 (1), ss. 195-203.
- Aytar S.and Pehlivan, S. (2007) Statistical cluster and extreme limit points of sequences of fuzzy numbers, Information Sciences, 177, 3290--3296.
- Altin, Y., Et, M.and Çolak, R. (2006). Lacunary statistical and lacunary strongly convergence of generalized difference sequences of fuzzy numbers, Computers & Mathematics with Applications, 52 (6-7), ss1011-1020.
- Karakaş, A., Altin, Y. and Altinok, H. (2014). On generalized statistical convergence of order β-of sequences of fuzzy numbers, Journa of Intelligent &. Fuzzy Systems, 26 (4), ss. 1909-1917.
- Zygmund, A. (1968). Trigonometric series: Vols. I, II. Cambridge University Press, London-New York.
- Steinhaus, H. (1951). Surla convergence ordinarie et la convergence asymptotique, Colloquium Mathematicum, 2, ss. 73-74.
- Fast, H. (1951). Sur la convergence statistique, Colloquium Mathematicum, 2, ss. 241-244.
- Fridy, J.A. (1985). On the statistical convergence, Analysis, 5, ss. 301-313.
- Šalát, T. (1980). On statistically convergent sequences of real numbers. Mathematica Slovaca, 30 (2), ss. 139-150.
- Connor, J.S (1988). The statistical and strong p-Cesàro convergence of sequences, Analysis, 8 (1-2), ss. 47-63.
- Tripathy, B.C. and Sen, M. (2001). On generalized statistically convergent sequences, Indian Journal of Pure Applied Mathematics, 32 (11), ss.1689-1694.
- Gadjiev, A. D. and Orhan, C.(2002). Some approximation theorems via statistical convergence, Rocky Mountain Journal of Mathematics, 32 (1), ss. 129-138.
- Çolak, R. (2010). Statistical convergence of order α, Modern Methods in Analysis and Its Applications, Anamaya Pub., New Delhi, India, ss. 121-138.
- Freedman, A.R., Sember, J.J. and Raphael, M. (1978). "Some Cesaro-type summability spaces", Proc. Lond. Math. Soc., 37, 508-520.
- Fridy, J. A. and Orhan, C. (1993). Lacunary Statistical Convergence, Pacific J. Math. 160 (1) 43-51.
- Duman, O. and Orhan, C. (2004). μ-statistically convergent function sequences, Czechoslovak Mathematical Journal. 54 (129) no. 2, ss. 413-422.
- Gökhan, A. and Güngör, M. (2002). On pointwise statistical convergence, Indian Journal of Pure Applied Mathematics, 33 (9), ss. 1379-1384.
- Çinar, M.; Karakaş, M., Et, M. (2013). On pointwise and uniform statistical convergence of order α for sequences of functions, Fixed Point Theory and Application, 33, 11 pp.
- Nuray, F., (1998). Lacunary statistical convergence of sequences of Fuzzy numbers, Fuzzy Sets Syst., 99 353-355.
- Şengül, H. and Et, M. (2014). On lacunary statistical convergence of order α, Acta Math. Sci. Ser. B Engl. Ed. 34 (2), 473-482.
- Bhardwaj, V. K. and Dhawan, S. (2016). Density by moduli and lacunary statistical convergence, Abstr. Appl. Anal., Art. ID 9365037, 11 pp.
- Das, G., and Mishra, S.K. (1983). Banach limits and lacunary strong almost convegence, J.Orissa Math. Soc.2, 61-70.
- Puri, M. L. and Ralescu, D.A. (1986). Fuzzy random variables, Journal of Mathematical Analysis and Applications, 114, ss. 409-422.
- Mursaleen, M. and Başarır, M. (2003). On some new sequence spaces of fuzzy numbers, Indian Journal of Pure and Applied Mathematics, 34 (9), ss.1351-1357.
- Matloka, M. (1987). Fuzzy mappings- sequences and series, Busefal, 30, ss.18-25.
- Altin, Y. Et, M. ve Tripathy, B. C. (2007). On pointwise statistical convergence of sequences of fuzzy mappings, Journal Fuzzy Mathematics, 15 (2), ss. 425-433.
- Et, M., Tripathy, B.C. ve Dutta, A.J. (2014). On pointwise statistical convergence of order α-of sequences of fuzzy mappings, Kuwait Journal of Science, 41 (3), ss. 17-30.
- Et, M. (2014). On pointwise λ-statistical convergence of order α-of sequences of fuzzy mappings, Filomat, 28 (6), ss.1271-1279.
- Gong, Z., Zhang, L.ve Zhu, X. (2015). The statistical convergence for sequences of fuzzy-number-valued functions, Information Sciences, 295, ss. 182-195.
- Srivastava, P.D. ve Ojha, S. (2014). λ-Statistical convergence of fuzzy numbers and fuzzy functions of order θ, Soft Computing, 18,ss. 1027-1032.
- Hung, N. V., Tam, V. M., Tuan, N. H.and O'Regan, D. (2020). Convergence analysis of solution sets for fuzzy optimization problems, Journal of Computational and Applied Mathematics, 369, 112615, 11 pp.
- Hazarika, B. (2017). Pointwise ideal convergence and Uniformly ideal convergence of sequence of fuzzy valued functions, Journal of İntelligent & Fuzzy Systems, 32 (3), ss. 2665-2677.