A right-pointing arrow with an upper half-barb, commonly used to denote weak convergence or specialized mappings in analysis.
Examples
Weak convergence in functional analysis
x_n \rightharpoonup x \text{ in } X
Vector field notation
\vec{F}(x,y) = x\mathbf{i} \rightharpoonup y\mathbf{j}
Partial function mapping
f: A \rightharpoonup B