Generalized weak contractions with control functions on metric and normed interval spaces

In this paper, we discuss some near-fixed point theorems with control functions for mappings that are specifically generalized weakly contraction in metric and normed interval spaces. We prove the existence and uniqueness of near-fixed points and common near-fixed points for these mappings. Moreover, we provide some examples to demonstrate the validity of our extensions.

Keywords:

Alternating distance functions , Contractive mappings , Metric interval spaces , Near fixed points , Normed interval spaces , null set