New fixed point results in controlled metric type spaces based on new contractive conditions

Abstract

In the present work, we will establish and prove some fixed point theorems for mappings that satisfy a set of conditions in controlled metric type spaces introduced by Mlaiki et al. [N. Mlaiki, H. Aydi, N. Souayah, T. Abdeljawad, Controlled metric type spaces and the related contraction principle. Mathematics 2018, 6,194]. Our technique in constructing our new contraction conditions is to insert the control function θ(u,l) that appears on the right hand side of the triangular inequality of the definition of the controlled metric spaces in the right hand side of our proposed contraction conditions. Our results enrich the field of fixed point theory with novel findings that generalize many findings found in the literature. We provide an example to show the usefulness of our results. Also, we present an application to our results to show their significance.

Keywords

• fixed point
• controlled metric space of type (γ，β)
• extended b-metric space