1. Invent new sufficient conditions for the existence of fixed point for new single valued mapping in b-metric spaces and also provide some example to show generality of our result.
2. To establish new knowledge and fixed point theorems for multi-valued operator.
Also, state some illustrative examples to claim that our results properly generalizes some results in literature are given.
3. To apply our results to investigate fixed point problems in various situation as problems in space endowed with an arbitrary binary relation, problems in partially ordered space and problems in space endowed with directed graph.
4. To obtain and study the coupled fixed point and best proximity point problems without some conditions for single valued mapping and multi-valued operator.
