Sentence examples for mapping and prove from inspiring English sources

With a motivation to remove this strong condition, in this paper we introduce a new iteration scheme for a pair of hybrid mapping and prove some convergence theorems for generalized nonexpansive mappings.

Later, we introduce the notion of a G - -Meir-Keeler contrandive maprove and prove some fixed point theorems for this class of mappings in the setting of G-metric spaces.

In this paper, we introduce the concept of a mixed g-monotone mapping and prove coupled coincidence and common coupled fixed point theorems for mappings under ϕ-contractive conditions in partially ordered generalized fuzzy metric spaces.

We introduce the notion of a modified α-ϕ-fuzzy contractive mapping and prove some results in fuzzy metric spaces for such kind of mappings.

In this paper, we introduce the concept of a mixed g-monotone mapping, which is a generalization of the mixed monotone mapping, and prove coupled coincidence point and coupled common fixed point theorems for mappings under ϕ-contractive conditions in partially ordered G-fuzzy metric spaces.

In this section, we define the notion of almost generalized s -contractive mapping and prove our new results.

In 1981, Heilpern [2] used the concept of fuzzy sets and introduced a class of fuzzy mappings, which is a generalization of the set-valued mapping, and proved a fixed point theorem for fuzzy contraction mappings in metric linear spaces.

Most recently, Samet et al. [12, 15] defined an α-ψ-contractive and α-admissible mapping and proved fixed point theorems for such mappings in complete metric spaces.

Most recently, Samet et al. [36] have defined α-ψ-contractive and α-admissible mapping and proved fixed point theorems for such mappings in complete metric spaces.

On the other hand, Bhaskar and Lakshmikantham have introduced the concept called mixed monotone mapping and proved coupled fixed point theorems for mappings satisfying the mixed monotone property, which is used to investigate a large class of problems, and they discussed the existence and uniqueness of a solution for a periodic boundary value problem.

On the other hand, Bhaskar and Lakshmikantham [32] introduced the notions of a mixed monotone mapping and proved some coupled fixed point theorems for mappings satisfying the mixed monotone property.