Fixed Point Theorem for Set Valued Mapping with Rational Condition

Liqaa J.  Khaleel; Buthainah A. A.  Ahmed

doi:10.24996/ijs.2020.61.4.12

Authors

Liqaa J. Khaleel Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Buthainah A. A. Ahmed Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2020.61.4.12

Keywords:

partial metric space, Hausdorff metric, usual metric, lower semi continuous function and Banach contraction principle

Abstract

In this paper, we generalized the principle of Banach contractive to the relative formula and then used this formula to prove that the set valued mapping has a fixed point in a complete partial metric space. We also showed that the set-valued mapping can have a fixed point in a complete partial metric space without satisfying the contraction condition. Additionally, we justified an example for our proof.