Sentence examples for interesting fixed from inspiring English sources

Several interesting fixed points results have emerged as a result of such study.

Nadler [21] and Assad and Kirk [22] established some interesting fixed point results for set valued and multivalued contraction mappings.

The concepts of fixed point theory and graph theory were combined by Espinola and Kirk [17] to prove some interesting fixed point theorems in R-trees.

Let ((X,d)) be a complete metric space and (T:X rightarrow operatorname{CB}(X)) be a multi-valued mapping such that H(Tx,Ty) leq kd x,y) (1.1) for all (x,y in X), where (kin[0,1)). Then T has at least one fixed point. Since Nadler's fixed point theorem, a number of authors have published many interesting fixed point theorems in several ways (see [2 4] and references therein).

In 1969, Boyd and Wong proved a very interesting fixed point theorem.

From Theorem 2.6, we can obtain the following interesting fixed point theorem.

In 2006, Bhaskar and Lakshmikantham [6] initiated the idea of a coupled fixed point in partially ordered metric spaces and proved some interesting coupled fixed point theorems for a mapping satisfying the mixed monotone property.

Furthermore, they established some interesting coupled fixed point theorems.

Some authors obtained some interesting coupled fixed point theorems in G-metric spaces (see e.g. [15 18]).

In 2006, Bhaskar and Lakshmikantham [2] first proved the following interesting coupled fixed point theorem in partially ordered metric spaces.

In 1987, the idea of coupled fixed point was initiated by Guo and Lakshmikantham [6]; it was also followed by Bhaskar and Lakshmikantham [7] wherein authors proved some interesting coupled fixed point theorems for mappings satisfying the mixed monotone property.