Sentence examples for a generalization of modular from inspiring English sources

A generalization of modular transfer line designing problem is addressed.

The notion of modular spaces, as a generalization of metric spaces, was introduced by Nakano [1] in 1950 in connection with the theory of order spaces and redefined and generalized by Musielak and Orlicz [2] in 1959.

As usual, logx is the natural logarithm of x ∈ R +, B is the usual beta function, while B denotes the incomplete beta function defined by B ( x ; a, b ) = ∫ 0 x t a − 1 ( 1 − t ) b − 1 d t, x ∈ [ 0, 1 ], a, b > 0. Our first result is a generalization of inequality (1.2) to an arbitrary modular function Φ : I ⊆ R → R such that a 1 Ψ ( x ) ≤ Φ ( x ) ≤ a 2 Ψ ( x ), x ∈ I, (2.1).

We give a generalization of the Banach contraction principle on a modular metric space endowed with a graph.

Musielak and Orlicz [2] in 1959 redefined and generalized it to obtain a generalization of the classical function spaces L p. Khamsi et al. [3] investigated the fixed point results in modular function spaces.

Taking (alpha x, y) = 1) for all (x, y in C) in Theorem 3.2, we get the following result, which is a generalization of Theorem 4 of Abbas et al. [14] in the setting of a modular metric.

In this article, we prove a generalization of Geraghty's theorem which also improves the result of Eshagi Gordji et al. [13] under the influence of a modular metric space.

Orthogonal arrays are a generalization of orthogonal Latin squares.

Complex numbers are a generalization of the familiar decimal numbers that mathematicians call the real numbers.

A generalization of the Th.

Furthermore, a generalization of Th.