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.
We prove two Theorems on approximation of functions belonging to Lipschitz classLip(α,p)inLp-norm using Cesàro submethod. Further we discuss few corollaries of our Theorems and compare them with the existing results. We also note that our results give sharper estimates than the estimates in some of the known results.
Trigonometric approximation of functions $f(x,y)$ of generalized Lipschitz class by double Hausdorff matrix summability method
