Sentence examples for by using a generalization from inspiring English sources

We prove Turán-type inequalities for some special functions by using a generalization of the Schwarz inequality.

Abdulkadir [20] studied the case (a=b=0), (varrho_{0}, varrho _{1}equiv0) and drew some conclusions by using a generalization of the Leggett-Williams fixed point theorem.

A new generalization of the weighted majorization theorem for n-convex functions is given, by using a generalization of Taylor's formula.

The purpose of this paper is to prove some existence theorems for fixed point problem by using a generalization of metric distance, namely u-distance.

By using a generalization of the Leggett-Williams fixed point theorem due to Bai and Ge, we prove that a boundary value problem has at least three positive solutions.

Its properties are calculated by using a generalization of the shape function concept from finite elements in which the shape functions (displacement fields) in the special element are determined by performing static stress analyses on the special element's substructure.

By using a useful generalization of Krasnoselskii's fixed point theorem due to Dhage [28], we prove an existence result for the initial value problem (1.2).

It is shown that various multicomponent diffusion equations can be written in the generalized Maxwell Stefan (MS) form by using a simple generalization of the inversion method presented in a publication by Merk [1959. Applied Scientific Research A 8, 73 99].

By using a natural generalization of the concept of a set, the fuzzy set, which was introduced initially by Zadeh [1], considering mathematical programming problems which are expressed as optimizing some goal function given certain constraints, this be relaxed by means of a subjective gradation.

The geometric imperfection is obtained from the buckling mode by a suitable scaling procedure using a generalization of Dutheil's method.

Another proof, using a generalization of the Poincaré-Birkhoff theorem, was suggested by Franks [6].