Sentence examples for established a generalization of from inspiring English sources

Following the concept of a Δ-density for a subset of a time scale, we established a generalization of these notions which are called Δ-limit and Δ-cluster points for a function defined on a time scale (mathbb{T}).

Cohen and Mullen [2] established a generalization of Golomb's conjecture by proving the existence of q 0 > 0 such that, whenever q > q 0, there exist α, β ∈ F q with γ α + δ β = ε, where γ, δ and ε are arbitrary non-zero elements of F q.

Zhang and Sun [2] established a generalization of the Leggett-Williams fixed point theorem and studied the existence of multiple nondecreasing positive solutions for problem (1) by replacing (q(t)f t,u(t),u'(t))) with (f t,u(t),u'(t),u t))).

We establish a generalization of several results.

Best proximity point theorems establish a generalization of fixed points by considering self-mappings.

We establish a generalization of the inequality introduced by Mitrinović and Pečarić in 1988.

We aim at establishing a generalization of the Plemelj-Sokhotzki formulae to the case of -monogenic matrix functions.

In this section, we establish a generalization of Dunkl-Williams inequality and its reverse in 2-normed spaces.

In the third section, we also establish a generalization of (1.4) for the degenerate Bernoulli polynomial β n ( λ, x ) (see, e.g., [3]).

In the present section, we shall establish a generalization of Diaz-Margolis's fixed point theorem (i.e. Theorem 1.1) for (mathcal{MT} -functions in the setting of comathcal{MT} -functionsrin spaces.

By introducing some parameters, we establish a generalization of the Hilbert-type integral inequality in the whole plane with the homogeneous kernel of degree − 2 λ and the best constant factor which involves the hypergeometric function.