Sentence examples for been generalized and improved from inspiring English sources

These results have been generalized and improved in a variety of ways; see [8 14].

In last ten years or so, the problem (EP) has been generalized and improved to find a common element of the set of fixed points of a nonlinear operator and the set of solutions of the problem (EP).

In the recent past, this result of Ran and Reurings has been generalized and improved by several researchers and by now there exists a considerable literature around this theorem.

In the course of the last century, this theorem has been generalized and improved by numerous researchers chiefly by replacing contraction mappings with a relatively more general contractive mappings and this practice is still going on.

It is well known that the Banach contraction principle (see [1]) plays an important role in various fields of applied mathematical analysis and scientific applications, and it has been generalized and improved in many different directions.

This approach has been generalized and improved to achieve higher accuracy around recombination sites in e.g. SLRP [ 61], ANCHAP [ 62] and other methods [ 63].

Some earlier results are generalized and improved.

Some recent results in the literature are generalized and improved.

Thus the results in [12] are generalized and improved significantly.

Some well-known results are generalized and improved.

Thus, some known results are generalized and improved.