Sentence examples for by giving a generalization from inspiring English sources
Precisely, Sehgal and Bharucha-Reid [9] introduced probabilistic q-contractions and proved corresponding unique fixed point results by giving a generalization of the classical Banach fixed point principle.
Fang [11] introduced the concept of 'F-type topological spaces' generating the topology by families of quasi-metrics and gave a generalization of Ekeland's variational principle.
In 1978, Rassias [3] gave a generalization of Hyers' theorem by allowing the Cauchy difference to be controlled by a sum of powers like (1.3).
In [6], the authors give a generalization of Theorem 1.2 by considering a non-self mapping, and they get the following theorem.
In [2], the authors give a generalization of Theorem 1.2 by considering a nonself map and they get the following theorem.
The stability result concerning derivations between operator algebras was first obtained by Šemrl in [5], Badora in [6] gave a generalization of Bourgin's result [7].
are true if and only if α ≤ 0 and β ≥ 3 / 5. Now we give a generalization of inequalities (1.4) given by Zhu [15].
= ∂ n ∂ t n F λ, q, χ ( x, t, u, a, b ) | t = 0. Now we give a generalization of the Raabe formula by the following theorem.
Motivated by their works, our goal in this article is to give a generalization of related results in Sprößig [2] to the variable exponent setting.
In 1949, 1950, and 1978, Bourgin [3], Aoki [4], and Rassias [5] gave a generalization of it under the conditions bounded by variables.
