Sentence examples for mappings given by from inspiring English sources

Take the mappings given by,.

Consider the mappings given by,,.

In this paper, we generalize the contractive condition for multi-valued mappings given by Asl, Rezapour and Shahzad in 2012.

In order to formulate the results, we extend to multivalued mappings the notion of weakly isotone increasing mappings given by Vetro [[28], Definition 4.2].

Let (f, g:mathbb {D}to mathbb {D}) be the K-quasiconformal mappings given by (f(re^{itheta}) = r^{frac{1}{K}} e^{itheta}) and (g(re^{itheta}) = r^{K} e^{itheta}).

Heilpern [1] introduced the concept of fuzzy mappings in a metric space and proved a fixed point theorem for fuzzy contraction mappings as a generalization of the fixed point theorem for multivalued mappings given by Nadler [7].

A generalized version of the theorem of Hyers for approximately additive mappings was given by Aoki in [3] and for approximate linear mappings was presented by Rassias in [4] by considering the case when the left-hand side of (1.1) is controlled by a sum of powers of norms.

The inner product between feature mappings is given by the positive definite kernel function.

In 1978, a generalized solution for approximately linear mappings was given by Th.

In 1978, a generalized solution for approximately linear mappings was given by Th.M. Rassias [5].

One of the most celebrated results about multivalued mappings was given by Lim [2] in 1974.