Generalized uncertainty principle with maximal observable momentum and no minimal length indeterminacy

We present a novel generalization of the Heisenberg uncertainty principle which introduces existence maximal observable momentum and at same time does not entail minimal indeterminacy in position. The above result is an exact generalized (GUP), valid all energy scales. For small values deformation parameter $\beta$, our ansatz consistent with usual expression for GUP borrowed from string theory, doubly special relativity other quantum gravity candidates that provide $\beta$ negative sign. As preliminary analysis, we study implications this new model on some mechanical applications black hole thermodynamics.