An equivalent reformulation of summability by weighted mean methods

✍ Scribed by Ferenc Móricz; Billy E. Rhoades

• Book ID: 104156121
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 293 KB
• Volume: 268
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(97)00039-6

✦ Synopsis

We prove an equivalent definition of sumnmbility of a numerical series by a weighted mean method in terms of ordinary convergence of another series. Our result includes a classical one by Hardy as a particular case. In the proof we make intrinsic use of infinite matrices, and our proof is therefore different from Hardy's.