Sentence examples for mapping of integral from inspiring English sources

More precisely, we examine the contractive mapping of integral type given in [11] by using α-admissible mappings.

Remark 2.1 It is evident that if T : X → X is an α-ψ-contractive mapping of integral type, then T is a generalized α-ψ-contractive mapping of integral types I and II.

Branciari [1] was the first to study the existence of fixed points for the contractive mapping of integral type.

Branciari [2] gave an integral version of the Banach contraction principles and proved fixed point theorem for a single-valued contractive mapping of integral type in metric space.

In order to ensure the uniqueness of a fixed point of a generalized α-ψ-contractive mapping of integral type II, we need an additional condition (U) defined in the previous section.

In 2002, Branciari [1] introduced the notion of contractive mappings of integral type in metric spaces and proved the following fixed point theorem for the contractive mapping of integral type, which is a nice generalization of the Banach contraction principle.

In this section, we prove Theorem 2.2 for a quasi-contraction map of integral type.

Considerable interest of researchers is focused on the study of mapping properties of integral operators defined on (quasi metric measure spaces.

The results for both groups of data include correction of the individual maps based on consensus analysis and building of integral maps.

The cavity surface and the fringe boundary which is elevated above the cavity position, are found through conformal mapping and the use of integral representations of non-standard mixed boundary-value problems.

As a consequence of Theorem 2.1, we obtain following fixed point result for a mapping satisfying contractive conditions of integral type in a complete partial metric space X.