The phrase "a remarkable generalization of" is correct and usable in written English.
It can be used when discussing a concept or theory that extends or broadens the understanding of a particular subject.
Example: "This study presents a remarkable generalization of previous research, highlighting new patterns in the data."
Alternatives: "an impressive extension of" or "a significant broadening of".
On the other hand, Suzuki [5] recently obtained a remarkable generalization of the Banach contraction theorem which itself has been extended and generalized on various settings (see, e.g, [6 15]).
As a corollary, a remarkable generalization of Rieszʼs theorem is obtained.
A remarkable generalization of the strong law of large numbers is the ergodic theorem: if X t), t = 0, 1,… for the discrete case or 0 ≤ t < ∞ for the continuous case, is a stationary process such that E[X(0)] is finite, then with probability 1 the average if t is continuous, converges to a limit as s → ∞.
In 1978, Rassias [25] provided a remarkable generalization of the Ulam-Hyers stability of mappings by considering variables.
Later, Rassias in [3] provided a remarkable generalization of the Hyers' result by allowing the Cauchy difference to be bounded for the first time, in the subject of functional equations and inequalities.
Definition 7.1 and Lemma 7.3 have a remarkable generalization.
The following remarkable generalization of the classical Banach contraction theorem due to Suzuki [2], states the following.
This not only leads to technical improvements and clarifications of the proofs, but also to remarkable generalizations of known results.
The exact mathematical description of these approximations gives remarkable generalizations of the central limit theorem from sequences of random variables to sequences of random functions.
Hadamard's inequality for convex functions has received renewed attention in recent years and a remarkable variety of refinements and generalizations have been found (see, for example, [1 4]).
One of the remarkable generalizations, known as Φ-contraction, was given by Boyd and Wong [1] in 1969.
