On pointwise statistical convergence of order α of sequences of fuzzy mappings

Authors

  • MIKAIL ET Department of Mathematics, Frat University, 23119 Elazig, Turkey
  • BINOD CHANDRA TRIPATHY Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Paschim Boragaon, Garchuk, Guwahati-781035, Assam India
  • AMAR JOYTI DUTTA Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Paschim Boragaon, Garchuk, Guwahati-781035, Assam India

Keywords:

Cesaro summability, pointwise statistical convergence, sequences of fuzzy mappings

Abstract

In this paper, we introduce the concept of pointwise statistical convergence of order α of sequences of fuzzy mappings. Furthermore we give the concept of α-statistically Cauchy sequence for sequences of fuzzy mappings and prove that it is equivalent to pointwise statistical convergence of order α of sequences of fuzzy mappings. Also some relations between Sβ(F)-statistical convergence and strong w F)-summability are given.

References

Altın Y., Et, M. & Çolak, R. 2006. Lacunary statistical and lacunary strongly convergence of generalized difference sequences of fuzzy numbers. Computers and Mathematics with Applications 52(6-7): 1011-1020.

Altın, Y., Et, M. & Tripathy, B. C. 2007. On pointwise statistical convergence of sequences of fuzzy mappings. Journal of Fuzzy Mathematics 15(2): 425-533.

Altın, Y., Et, M. & Basarır, M. 2007. On some generalized difference sequences of fuzzy numbers. Kuwait Journal of Science and Engineering 34(1A): 1-14.

Altınok, H., Çolak, R. & Et, M. 2009. -difference sequence spaces of fuzzy numbers. Fuzzy Sets and Systems 160(21): 3128-3139.

Burgin, M. 2000. Theory of fuzzy limits. Fuzzy Sets and Systems 115: 433-443.

Çolak, R., Altınok, H. & Et, M. 2009. Generalized difference sequences of fuzzy numbers. Chaos, Solitons and Fractals 40(3): 1106-1117.

Çolak, R. 2010. Statistical convergence of order Modern Methods in Analysis and Its Applications, New Delhi India: Anamaya Publishers 121-129.

Connor, J. S. 1988. The Statistical and strong Cesàro convergence of sequences. Analysis 8: 47-63.

Diamond, P. & Kloeden, P. 1990. Metric spaces of fuzzy sets. Fuzzy Sets and Systems 35(2): 241-249.

Et, M. & Nuray, F. 2001. statistical convergence. Indian Journal of Pure and Applied Mathematics 32(6): 961-969.

Et, M. 2003. Strongly almost summable difference sequences of order defined by a modulus. Studia Scientiarum Mathematicarum Hungarica 40(4): 463-476.

Et, M., Altın, Y., Choudhary B. & Tripathy B. C. 2006. On some classes of sequences defined by sequences of Orlicz functions. Mathematical Inequalities and Applications 9(2): 335-342.

Fast, H. 1951. Sur la convergence statistique. Colloquium Mathematicum 2: 241-244.

Fridy, J. A. 1985. On statistical convergence. Analysis 5: 301-313.

Gadjiev, A. D. & Orhan, C. 2002. Some approximation theorems via statistical convergence. Rocky Mountain Journal of Mathematics 32(1): 129-138.

Gökhan, A., Et, M. & Mursaleen, M. 2009. Almost lacunary statistical and strongly almost lacunary convergence of sequences of fuzzy numbers. Mathematical and Computer Modelling 49(3-4): 548-555.

Gökhan, A. & Güngör, M. 2002. On pointwise statistical convergence. Indian Journal of Pure and Applied Mathematics 33(9): 1379-1384.

Güngör, M., Et, M. & Altın, Y. 2004. Strongly summable sequences defined by Orlicz functions. Applied Mathematics and Computation 157(2): 561-571.

Işık, M. 2011. Strongly almost summable sequences. Mathematica Slovaca 61(5): 779-788.

Lakshmikantham, V. & Mohapatra, R. N. 2003. Theory of Fuzzy Differential Equations and Inclusions, Taylor and Francis. New York.

Matloka, M. 1987. Fuzzy mappings-sequences and series. BUSEFAL 30: 18-25.

Mursaleen, M. & Başarır, M. 2003. On some new sequence spaces of fuzzy numbers. Indian Journal of Pure and Applied Mathematics 34: 1351-1357.

Rath, D. & Tripathy, B. C. 1994. On statistically convergent and statistically Cauchy sequences. Indian Journal of Pure and Applied Mathematics 25(4): 381-386.

Šalát, T. 1980. On statistically convergent sequences of real numbers. Mathematica Slovaca 30: 139-150.

Schoenberg, I. J. 1959. The integrability of certain functions and related summability methods. American Mathematical Monthly 66: 361-375.

Steinhaus, H. 1951. Sur la convergence ordinaire et la convergence asymptotique. Colloquium Mathematicum 2: 73-74.

Talo, Ö. & Başar, F. 2009. Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations. Computers and Mathematics with Applications 58(4): 717-733.

Tripathy, B. C. & Sarma, B. 2011. Some double sequence spaces of fuzzy numbers defined by Orlicz functions. Acta Mathematica Scientia Series B English Edition 31(1): 134-140.

Tripathy, B. C. 1997. Matrix transformations between some class of sequences. Journal of Mathematical Analysis and Applications 206(2): 448-450.

Tripathy, B. C. & Dutta, A. J. 2007. On fuzzy real-valued double sequence space . Mathematical and Computer Modelling 46(9-10): 1294-1299.

Tripathy, B. C. & Dutta, A. J. 2006. Bounded variation double sequence space of fuzzy numbers. Computers and Mathematics with Applications 59(2): 1031-1037.

Zadeh, L. A. 1965. Fuzzy sets. Information and Control 8: 338-353.

Zygmund, A. 1979. Trigonometric Series. Cambridge University Press. Cambridge, UK.

Downloads

Published

29-09-2014