Geodesic
Tauberian theorems for the Cesàro summability method of regularly generated double integrals
Filomat, Tome 37 (2023) no. 9, p. 2969

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DOI

For a continuous function 1 over R2+ := [1,∞) × [1,∞), we denote its integral over [1, x] × [1, y] by h(x, y) = ∫ x 1 ∫ y 1 1(u, v)dudv and its (C, 1, 1) mean, the average of h(x, y) over [1, x] × [1, y], by t(h(x, y)) = (xy)−1 ∫ x 1 ∫ y 1 h(u, v)dudv. Analogously, the other means (C, 1, 0) and (C, 0, 1) can be defined. In this paper, we introduce the concept of regularly generated double integrals in senses (1, 1), (1, 0) and (0, 1) and obtain Tauberian conditions in terms of the regularly generated double integrals in senses (1, 1), (1, 0) and (0, 1) under which convergence of h(x, y) follows from that of t(h(x, y)).
DOI : 10.2298/FIL2309969F
Classification : 40A10, 40C10, 40E05
Keywords: Slow oscillations in senses (1, 0) and (0, 1), strong slow oscillations in senses (1, 0) and (0, 1), Tauberian conditions and theorems, Cesàro summability method, improper double integral, regularly generated integrals 
Gökşen Fındık; Ìbrahim Çanak. Tauberian theorems for the Cesàro summability method of regularly generated double integrals. Filomat, Tome 37 (2023) no. 9, p. 2969 . doi: 10.2298/FIL2309969F
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     author = {G\"ok\c{s}en F{\i}nd{\i}k and \`Ibrahim \c{C}anak},
     title = {Tauberian theorems for the {Ces\`aro} summability method of regularly generated double integrals},
     journal = {Filomat},
     pages = {2969 },
     year = {2023},
     volume = {37},
     number = {9},
     doi = {10.2298/FIL2309969F},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2309969F/}
}
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