In this note we show the somewhat surprising fact that proof of `if part' distinguished characterizations metric completeness due to Kirk, and Suzuki Takahashi, respectively, can be deduced in a straightforward manner from Hu's theorem space is complete if only any Banach contraction on bounded closed subsets thereof has fixed point. We also take advantage approach easily deduce characterizatio...

In this paper, we establish a fixed point theorem for controlled rectangular $b-$metric spaces mappings that satisfy $(\psi, \phi)-$contractive mappings. Also, give an application of our results as integral equation.

In this paper, we introduce the notion of an extended metric space ($p$-metric space) as a new generalization of the concept of $b$-metric space. Also, we present the concept of $(psi ,varphi )_{Omega}$-contractive mappings and we establish some fixed point results for this class of mappings in ordered complete $p$-metric spaces. Our results generalize several well...

‎In this paper‎, ‎we introduce $alpha$-$psi$-contractive mapping in partially ordered sets and construct fixed point theorems to solve a first-order ordinary differential equation by existence of its lower solution.

‎in this paper‎, ‎we introduce $alpha$-$psi$-contractive mapping in partially ordered sets and construct fixed point theorems to solve a first-order ordinary differential equation by existence of its lower solution.