Almost $\alpha$-Hardy-Rogers-$F$-contractions and their applications


$\alpha$-admissible, $0$-complete, almost $\alpha$-Hardy-Rogers-$F$-contraction, partial metric space


The aim of this article is to introduce the notion of almost $\alpha$-Hardy-Rogers-$F$-contractions in the partial metric space and utilize it to establish the existence of a unique fixed point. Some examples are given to demonstrate the validity of our main result. Our results generalize classical and newer results in the literature. As an application, we solve the initial value problem of damped harmonic oscillator and a nonlinear fractional differential equation satisfying periodic boundary conditions, which demonstrates the importance of our contraction and provides motivation for such investigations.




How to Cite

Almost $\alpha$-Hardy-Rogers-$F$-contractions and their applications. (2019). Armenian Journal of Mathematics, 11(11), 1–19. Retrieved from