Sentence examples for mappings without the from inspiring English sources

Zhou [11] established the hybrid Ishikawa algorithm for Lipschitz pseudocontractive mappings without the compactness assumption.

Could we obtain some fixed point theorems for θ-contractive mappings without the conditions ((Theta_{2})) and ((Theta_{3}))?

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

In the paper [3], the authors gave simple and elementary proofs for the existence of fixed point theorems for asymptotic pointwise mappings without the use of ultrapowers.

In [3], the authors gave simple and elementary proofs for the existence of fixed point theorems for asymptotic pointwise mappings without the use of ultrapowers.

But it was still an open question whether or not this method can be employed to approximate fixed points of Lipschitz pseudocontractive mappings without the compactness assumption on K or T (see, e.g., [7 9]).

Afterwords, Abbas and Jungck [2] established the common fixed points for two mappings without exploiting the notion of continuity.

We are also able to prove the existence of a common fixed point of two mappings without using the continuity of S or T.

Is there any strong convergence theorem of Moudafi's type for quasi-nonexpansive mappings without using the demiclosedness principle in a Banach space E?

The aim of this section is to present coincidence points results for four mappings without satisfying the condition of continuity and commutation on cone metric type spaces with a non-normal cone.

In this section, we prove some fixed point theorems for expanding mappings without continuity in the following theorems.