The series
Σ
n
=
1
∞
a
n
\Sigma _{n = 1}^\infty {a_n}
is said to be summable
(
L
)
(L)
to
s
s
if
(
log
(
1
−
x
)
)
−
1
Σ
n
=
1
∞
s
n
x
n
+
1
/
n
{(\log (1 - x))^{ - 1}}\Sigma _{n = 1}^\infty {s_n}{x^{n + 1}}/n
, where
s
n
=
Σ
v
=
1
n
a
v
{s_n} = \Sigma _{v = 1}^n{a_v}
, converges for
0
≤
x
>
1
0 \leq x > 1
and tends to
s
s
when
x
→
1
−
x \to 1 -
. The aim of this paper is to discuss the relation between summability
(
L
)
(L)
and Riesz summability
(
R
,
log
n
,
κ
)
(R,\log n,\kappa )
. It is proved that
(
R
,
log
n
,
κ
)
⊆
(
L
)
(R,\log n,\kappa ) \subseteq (L)
holds for
0
≤
κ
≤
1
0 \leq \kappa \leq 1
and is false for
κ
>
1
\kappa > 1
. It is also proved that if
Σ
n
=
1
∞
a
n
=
s
(
L
)
\Sigma _{n = 1}^\infty {a_n} = s(L)
and bounded
(
R
,
log
n
,
κ
)
(R,\log n,\kappa )
for
κ
≥
0
\kappa \geq 0
then
Σ
n
=
1
∞
a
n
=
s
(
R
,
log
n
,
κ
+
δ
)
\Sigma _{n = 1}^\infty {a_n} = s(R,\log n,\kappa + \delta )
for every
δ
>
0
\delta > 0
.