Fixed Point Theorem for Set Valued Mapping with Rational Condition
partial metric space
Hausdorff metric
usual metric
lower semi continuous function and Banach contraction principle
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.
