Generalized linear methods and gap tauberian remainder theorems

References

• Boos , J. 2000 . Classical and modern methods in summability , Oxford University Press .
   Google Scholar
• Brezinski , C. 2000 . Numerical analysis 2000 . J. Comput. Appl. Math. , 122 (1–2) : 1 – 357 .
   Google Scholar
• Fridy , J.A. and Khan , M. K. 2003 . Statistical gap Tauberian theorems in metric spaces . J. Math. Anal. Appl. , 282 : 744 – 755 .
   Google Scholar
• Hardy , G. H. and Littlewood , J.E. 1926 . A further note on the converse of Abel's theorem . Proc. Lond. Math. Soc. , 25 : 219 – 236 .
   Google Scholar
• Kangro , G. 1956 . On matrix transformations of sequences in Banach spaces . Proc. Estonian Acad. Sci. Tech. Phys. Math. , 5 : 108 – 128 . (in Russian)
   Google Scholar
• Kangro , G. 1971 . Summability factors for the series λ‐bounded by the methods of Riesz and Cesàro . Acta Comment. Univ. Tartuensis , 277 : 136 – 154 . (in Russian)
   Google Scholar
• Knopp , K. 1971 . Theory and application of infinite series , Hafner .
   Google Scholar
• Krishnan , V.K. 1997 . A gap Tauberian theorem connecting Borel and Cesàro summabilities . J. Anal. , 5 : 9 – 24 .
   Google Scholar
• Lamp , Yu. and Tali , A. 1987 . The summability with rapidity of generalized sequences in Banach spaces . Acta Comment. Univ. Tartuensis , : 149 – 157 . (in Russian)
   Google Scholar
• Meronen , O. and Tammeraid , I. 2006 . Generalized Euler‐Knopp method and convergence acceleration . Math. Mod. and Anal. , 11 (1) : 87 – 94 .
   Google Scholar
• Meronen , O. and Tammeraid , I. 2007 . Generalized Nörlund method and convergence acceleration . Math. Mod. and Anal. , 12 (2) : 195 – 204 .
   Google Scholar
• Nappus , A. and Sõrmus , T. 1996 . Einige verallgemeinerte matrixverfahren . Proc. Estonian Acad. Sci. Phys. Math. , 45 ((2–3)) : 201 – 210 .
   Google Scholar
• Nemzer , D. 2004 . Generalized functions and an extended gap theorem . Indian J. Pure Appl. Math. , 35 (1) : 43 – 49 .
   Google Scholar
• Rangachari , M.S. 1996 . Remarks on gap Tauberian theorems . J. Indian Math. , 62 (1–4) : 145 – 148 .
   Google Scholar
• Sõrmus , T. 2000 . Tauberian theorems for generalized summability methods in Banach spaces . Proc. Estonian Acad. Sci. Phys. Math. , 49 (3) : 170 – 182 .
   Google Scholar
• Stadtmüller , U. and Tali , A. 2003 . Comparison of certain summability metdods by speed of convergence . Anal. Math. , 29 (3) : 227 – 242 .
   Google Scholar
• Tammeraid , I. 1971 . Tauberian remainder theorems for the Cesàro and Hölder methods of summability . Acta Comment. Univ. Tartuensis , 277 : 161 – 170 . (in Russian)
   Google Scholar
• Tammeraid , I. 1978 . Some Tauberian remainder theorems for gap series . Acta Comment. Univ. Tartuensis , : 52 – 54 . (in Russian)
   Google Scholar
• Tammeraid , I. 1989 . On a theorem of G. Kangro for gap series . Acta Comment. Univ. Tartuensis , : 74 – 79 . (in Russian)
   Google Scholar
• Tammeraid , I. 2001 . Convergence rate of iterative process and weighted means . Proc. of the OFEA'2001. Conference OFEA'2001 Saint Petersburg . 2001 , Russia. volume 2 , pp. 49 – 55 . 2002
   Google Scholar
• Tammeraid , I. 2003 . Convergence acceleration and linear methods . Math. Mod. and Anal. , 8 (1) : 87 – 92 .
   Google Scholar
• Tammeraid , I. 2003 . Generalized linear methods and convergence acceleration . Math. Mod. and Anal. , 8 (4) : 329 – 335 .
   Google Scholar
• Tammeraid , I. 2003 . Several remarks on acceleration of convergence using generalized linear methods of summability . J. Comput. Appl. Math. , 159 (2) : 365 – 373 .
   Web of Science ®Google Scholar
• Tammeraid , I. 2004 . Generalized Riesz method and convergence acceleration . Math. Mod. and Anal. , 9 (4) : 341 – 348 .
   Google Scholar
• Tietz , H. and Zeller , K. 1999 . The Tauberian gap theorems for the Abel method. Sequence spaces and applications , 130 – 134 . New Dehli : Narosa .
   Google Scholar
• Zeller , K. 1952 . Verallgemeinerte Matrix Transformationen . Math. Z. , 56 : 18 – 20 .
   Google Scholar
• Zeller , K. and Beekmann , W. 1970 . Theorie der limitierungsverfahren , Springer‐Verlag .
   Google Scholar