TAUBERIAN THEOREMS FOR GENERALIZED ABELIAN SUMMABILITY METHODS
Mathematica Moravica, Tome 2 (1998) no. 1.

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We introduce and study a significant generaliza­tion of Abel's summability method, and their corresponding limiting process. This leads to an analogue to Hardy-Littlewood Tauberian Theorem.The first section includes an introduction to some basic concepts of summability methods and a survey of classical and neoclassical results. In the second section a general summability method is designed and some related Tauberian theorems are established. In the third section higher order of Abel's summability methods are obtained as a special case of a general summability method and the general Littlewood theorem is proved for those summabil­ity methods. Finally we give Tauberian theorems corresponding to $(C, m)$-summability methods and present some further convergence theorems. 
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     author = {Ibrahim \c{C}anak},
     title = {TAUBERIAN  {THEOREMS}  {FOR} {GENERALIZED}  {ABELIAN}  {SUMMABILITY} {METHODS}},
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Ibrahim Çanak. TAUBERIAN  THEOREMS  FOR GENERALIZED  ABELIAN  SUMMABILITY METHODS. Mathematica Moravica, Tome 2 (1998) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_1998_2_1_a2/