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Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 8
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Original Articles

Statistically D-bounded sequences in probabilistic normed spaces

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Pages 1133-1142 | Received 10 Sep 2008, Accepted 27 May 2009, Published online: 21 Sep 2010

References

  • Menger , K . 1951 . Probabilistic geometry . Proc. Nat. Acad. Sci. USA , 37 : 226 – 229 .
  • Šerstnev , AN . 1963 . On the notion of a random normed space . Dokl. Akad. Nauk SSSR , 149 : 280 – 283 .
  • Alsina , C , Schweizer , B and Sklar , A . 1993 . On the definition of a probabilistic normed space . Aequationes Math. , 46 : 91 – 98 .
  • Schweizer , B and Sklar , A . 1983 . Probabilistic Metric Spaces , New York : Elsevier/North-Holland . (Reissued with an errata list, notes and supplemental bibliography by Dover Publications, New York, 2005)
  • Alsina , C , Schweizer , B and Sklar , A . 1997 . Continuity properties of probabilistic norms . J. Math. Anal. Appl. , 208 : 446 – 452 .
  • Lafuerza Guillén , B , Rodríguez Lallena , JA and Sempi , C . 1995 . Completion of probabilistic normed spaces . Int. J. Math. Math. Sci. , 18 : 649 – 652 .
  • Lafuerza Guillén , B , Rodríguez Lallena , JA and Sempi , C . 1997 . Some classes of probabilistic normed spaces . Rend. Mat. Appl. , 17 : 237 – 252 .
  • Lafuerza Guillén , B , Rodríguez Lallena , JA and Sempi , C . 1998 . Probabilistic norms for linear operators . J. Math. Anal. Appl. , 220 : 462 – 476 .
  • Lafuerza Guillén , B , Rodríguez Lallena , JA and Sempi , C . 1999 . A study of boundedness in probabilistic normed spaces . J. Math. Anal. Appl. , 232 : 183 – 196 .
  • Lafuerza Guillén , B . 2001 . D-bounded sets in probabilistic normed spaces and in their products . Rend. Mat. Appl. , 21 : 17 – 28 .
  • Lafuerza Guillén , B . 2004 . Finite products of probabilistic normed spaces . Rad. Mat. , 13 : 111 – 117 .
  • Saadati , R and Amini , M . 2005 . D-boundedness and D-compactness in finite dimensional probabilistic normed spaces . Proc. Indian Acad. Sci. (Math Sci). , 115 : 483 – 492 .
  • Sempi , C . 2006 . A short and partial history of probabilistic normed spaces . Mediterr. J. Math. , 3 : 283 – 300 .
  • Egbert , RJ . 1968 . Products and quotients of probabilistic metric spaces . Pacific J. Math. , 24 : 437 – 455 .
  • Şençimen , C and Pehlivan , S . 2008 . Strong statistical convergence in probabilistic metric spaces . Stoch. Anal. Appl. , 26 : 651 – 664 .
  • Fast , H . 1951 . Sur la convergence statistique . Colloq. Math. , 2 : 241 – 244 .
  • Steinhaus , H . 1951 . Sur la convergence ordinaire et la convergence asymptotique . Colloq. Math. , 2 : 73 – 74 .
  • Fridy , JA . 1985 . On statistical convergence . Analysis , 5 : 301 – 313 .
  • Fridy , JA and Orhan , C . 1997 . Statistical limit superior and limit inferior . Proc. Amer. Math. Soc. , 125 : 3625 – 3631 .
  • Tripathy , BC . 1997 . On statistically convergent and statistically bounded sequences . Bull. Malays. Math. Sci. Soc. (Second Series) , 20 : 31 – 33 .
  • Niven , I , Zuckerman , HS and Montgomery , HL . 1991 . An Introduction to the Theory of Numbers , New York : John Wiley & Sons .
  • Kostyrko , P , Šalát , T and Wilczyński , W . 2000 . ℐ-Convergence . Real Anal. Exchange , 26 : 669 – 685 .
  • Fridy , JA . 1993 . Statistical limit points . Proc. Amer. Math. Soc. , 118 : 1187 – 1192 .
  • Miller , HI . 1995 . A measure theoretical subsequence characterization of statistical convergence . Trans. Amer. Math. Soc. , 347 : 1811 – 1819 .
  • Šalát , T . 1980 . On statistically convergent sequences of real numbers . Math. Slovaca , 30 : 139 – 150 .
  • Pehlivan , S and Mamedov , MA . 2000 . Statistical cluster points and turnpike . Optimization , 48 : 93 – 106 .

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