Sentence examples for proved fixed from inspiring English sources

In recent years, many authors have proved fixed point and common fixed point theorems in fuzzy metric spaces.

They proved fixed point theorems for such mappings.

Thereafter, several authors worked in this direction and proved fixed point theorems in ordered metric spaces.

Afterward, other authors proved fixed point theorems in metric-type space [18 20].

The authors [26 28] proved fixed point theorems for multivalued maps in cone metric spaces.

In 2008, Kikkawa and Suzuki [9] proved fixed point theorems for some generalized Kannan mappings.

For such mappings, we prove fixed point theorems.

We prove fixed point theorems for such a mapping without the convexity of the domain.

We use chain methods to prove fixed point results for maximalizing mappings in posets.

Many authors used the extragradient method to prove fixed point theorem of nonlinear mappings.

In this paper, we prove fixed point theorems for Chatterjea mappings without the convexity of the domain.