AbstractIn this paper, we establish a new estimate for the degree of approximation of functions $f(x,y)$
f
(
x
,
y
)
belonging to the generalized Lipschitz class $Lip ((\xi _{1}, \xi _{2} );r )$
L
i
p
(
(
ξ
1
,
ξ
2
)
;
r
)
, $r \geq 1$
r
≥
1
, by double Hausdorff matrix summability means of double Fourier series. We also deduce the degree of approximation of functions from $Lip ((\alpha ,\beta );r )$
L
i
p
(
(
α
,
β
)
;
r
)
and $Lip(\alpha ,\beta )$
L
i
p
(
α
,
β
)
in the form of corollary. We establish some auxiliary results on trigonometric approximation for almost Euler means and $(C, \gamma , \delta )$
(
C
,
γ
,
δ
)
means.
Positive eigenvectors of positive polynomial operators on Banach spaces.