Almost lacunary statistical and strongly almost lacunary convergence of sequences of fuzzy numbers

The purpose of this paper is to introduce the concepts of almost lacunary statistical convergence and strongly almost lacunary convergence of sequences of fuzzy numbers. We give some relations related to these concepts. We establish some connections between strongly almost lacunary convergence and almost lacunary statistical convergence of sequences of fuzzy numbers. It is also shown that if a sequence of fuzzy numbers is strongly almost lacunary convergent with respect to an Orlicz function then it is almost lacunary statistical convergent.

[1]  Ayhan Esi,et al.  On some new paranormed sequence spaces of fuzzy numbers defined by Orlicz functions and statistical convergence , 2006 .

[2]  Salih Aytar,et al.  Statistically monotonic and statistically bounded sequences of fuzzy numbers , 2006, Inf. Sci..

[3]  Jeff Connor,et al.  Measures and Ideals of C* (X) , 1993 .

[4]  J. A. Fridy,et al.  Lacunary statistical convergence. , 1993 .

[5]  F. Smithies,et al.  Convex Functions and Orlicz Spaces , 1962, The Mathematical Gazette.

[6]  Bobby Schmidt,et al.  Fuzzy math , 2001 .

[7]  Allen R. Freedman,et al.  SOME CESARO-TYPE SUMMABILITY SPACES , 1978 .

[8]  Tibor Šalát,et al.  On statistically convergent sequences of real numbers , 1980 .

[9]  Fatih Nuray,et al.  Lacunary statistical convergence of sequences of fuzzy numbers , 1998, Fuzzy Sets Syst..

[10]  Binod Chandra Tripathy,et al.  On fuzzy real-valued double sequence space 2ℓpF , 2007, Math. Comput. Model..

[11]  Sudarsan Nanda,et al.  On sequences of fuzzy numbers , 1989 .

[12]  B. Choudhary,et al.  A sequence space defined by Orlicz functions , 2002 .

[13]  E. Savaş,et al.  On some new sequence spaces of invariant means defined by Orlicz functions , 2002 .

[14]  V. Lakshmikantham,et al.  Theory of Fuzzy Differential Equations and Inclusions , 2003 .

[15]  H. Fast,et al.  Sur la convergence statistique , 1951 .

[16]  Karl Lindberg,et al.  On subspaces of Orlicz sequences spaces , 1973 .

[17]  T. A. Chishti,et al.  Some new convergent sequences spaces defined by Orlicz functions and statistical convergence , 2001 .

[18]  J. A. Fridy,et al.  ON STATISTICAL CONVERGENCE , 1985 .

[19]  Francisco Gallego Lupiáñez,et al.  Intuitionistic fuzzy topological spaces , 2000 .

[20]  I. J. Schoenberg.  The Integrability of Certain Functions and Related Summability Methods , 1959 .

[21]  I. J. Maddox.  SPACES OF STRONGLY SUMMABLE SEQUENCES , 1967 .

[22]  I. J. Maddox.  A new type of convergence , 1978, Mathematical Proceedings of the Cambridge Philosophical Society.

[23]  P. Kloeden,et al.  Metric spaces of fuzzy sets , 1990 .

[24]  Manjul Gupta,et al.  Sequence spaces and series , 1981 .

[25]  Jeff Connor,et al.  A topological and functional analytic approach to statistical convergence , 1999 .

[26]  George G. Lorentz,et al.  A contribution to the theory of divergent sequences , 1948 .

[27]  Božidar V. Popović,et al.  Mathematical and Computer Modelling , 2011 .

[28]  Joram Lindenstrauss,et al.  On orlicz sequence spaces , 1971 .

[29]  Binod Chandra Tripathy,et al.  Matrix Transformation between Some Classes of Sequences , 1997 .

[30]  M. E. Naschie,et al.  A review of E infinity theory and the mass spectrum of high energy particle physics , 2004 .

[31]  Özer Talo,et al.  On the space bvp(F) of sequences of p-bounded variation of fuzzy numbers , 2008 .

[32]  Binod Chandra Tripathy,et al.  On a class of difference sequences related to the ℓp space defined by Orlicz functions , 2007 .