The phrase "a generalized point" is correct and usable in written English.
It can be used when discussing a broad or overarching idea that applies to multiple situations or examples.
Example: "In this discussion, we will focus on a generalized point that can be applied to various scenarios in our analysis."
Alternatives: "a broad statement" or "a general observation".
Firstly, an explicit form Green function for a generalized point load acted at an arbitrary point outside the hole is derived.
Secondly, the Green function for a generalized point load acted at the rim of the hole, as a special case, is obtained, and then a general solution for the case of arbitrarily distributed mechanical and electric loading on the hole surface is presented based on the superposition principle.
In [6, 7], Karsli obtained the pointwise convergence theorems and the rate of pointwise convergence theorems for a family of nonlinear singular integral operators at a μ-generalized Lebesgue point and a generalized Lebesgue point of f ∈ L 1 〈 a, b 〉, respectively.
The following two examples are simple applications to a generalized Lebesgue point and μ-generalized Lebesgue point of some functions that belong to (L_{1}(mathbb{R} ^{2})).
Then Rydzewska [3] conducted a similar study by changing the point to a μ-generalized Lebesgue point of f ∈ L 1 instead of a generalized Lebesgue point.
A point ( x ∗, y ∗ ) ∈ C × D is called a generalized saddle point of the mapping F if it satisfies F ( x, y ∗ ) ≼ U F ( x ∗, y ∗ ) ≼ U F ( x ∗, y ), for all x ∈ C and y ∈ D. It is equivalent, for all x ∈ C and y ∈ D, to u ≼ U w ∗ ≼ U v, for any u ∈ [ F ( x, y ∗ ) ], w ∗ ∈ [ F ( x ∗, y ∗ ) ] and v ∈ [ F ( x ∗, y ) ]. Definition 3.2 Let ( X, ≽ X ), ( Y, ≽ Y ) and ( U ; ≽ U ) be preordered sets.
Certain physical phenomena occurring at volcanic focal regions can be expressed in terms of a generalized seismic point source, as the sum of single forces and dipole forces (moment tensor).
F is order-cluster preserving on C × D. Then F has a generalized saddle point.
On the other hand, if we take (alpha=frac{1}{4}) and (p=1), then the origin is also a generalized Lebesgue point.
Following this work, Gadjiev [2] proved the pointwise convergence of operators of type (1.1) at a generalized Lebesgue point and established the pertinent convergence order.
Based on Taberski's study [1], Gadjiev [2] investigated both the pointwise convergence theorems and the order of pointwise convergence theorems for operators type (1) at a generalized Lebesgue point.
