I have a function which perform some mathematical operations and need a 16gb GPU system, But this function will not be triggered always and rest of time my system will not be in
You can't specify the runtime environment for AWS Lambda functions, so no, you can't require the presence of a GPU (in fact the physical machines AWS chooses to put into its Lambda pool will almost certainly not have one).
Your best bet would be to run the GPU-requiring function as a Batch job on a compute cluster configured to use p-type instances. The guide here might be helpful.
Currently lambda doesn't have GPU.
However, if you just need to do inference; the emulation via CPU works fine on AWS lambda; here is an article that goes into more details:
https://aws.amazon.com/blogs/machine-learning/how-to-deploy-deep-learning-models-with-aws-lambda-and-tensorflow/
Batch is a good solution for certain types of workload. Another option is GPUs on ECS, which could be used for running frequent tasks utilising GPU.