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

Authors

  • Anita Tomar V. S. K. C. Government P. G. College Dakpathar
  • Ritu Sharma V. S. K. C. Government P. G. College Dakpathar

DOI:

https://doi.org/10.52737/18291163-2019.11.11-1-19

Keywords:

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

Abstract

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.

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Published

2019-11-15 — Updated on 2022-09-15

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How to Cite

Almost $\alpha$-Hardy-Rogers-$F$-contractions and their applications. (2022). Armenian Journal of Mathematics, 11(11), 1-19. https://doi.org/10.52737/18291163-2019.11.11-1-19 (Original work published 2019)