Professor Hamkins already gave many interesting references. Let me add a few more.

Possibly, the work of Cummings-shelah [Cardinal invariants above the continuum](https://www.sciencedirect.com/science/article/pii/016800729500003Y?via%3Dihub) is the starting point for the study of generalizations of  cardinal invariants to the context of uncountable cardinals. In this paper, they prove the following:  If $λ↦(β(λ),δ(λ),μ(λ))$ is a class function from regular cardinals into the cube of cardinals satisfying $λ^+≤β(λ)=cf(β(λ))≤cf(δ(λ))≤δ(λ)≤μ(λ)$ and $cf(μ(λ))>λ$ for all $λ$, then there exists a model where $b(λ)=β(λ), \mathfrak{d}(λ)=δ(λ)$, and $2^λ=μ(λ)$ for all $λ$. 

for some other references see

- [Cardinal Invariants $\mathbf{b}_κ$ and $\mathbf{t}_κ$](http://shelah.logic.at/files/643.pdf).

- [Generalized Domination](https://deepblue.lib.umich.edu/bitstream/handle/2027.42/113539/danhath_1.pdf?sequence=1&isAllowed=y).

- [Two inequalities between cardinal invariants](https://arxiv.org/pdf/1505.06296.pdf)