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In this paper we provide some results on Ulam stability for the linear difference equation of order one in Banach spaces and we determine its best Ulam constant. The main result is applied to a process of loan amortization.

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Objective of the present study is to define the dynamic mechanical response of multi-story structures acted upon by wind. Structural response is associated to the dynamically applied wind and is approached by considering its three components: static, kinematic and energy states. Proposed objective is achieved by structural dynamic analyses performed on multi-story steel structures in elastic domain. The dynamic model is the multi-degree of freedom system associated to lateral story level displacements. Dynamic forces are computed from recorded velocities of wind through a simple velocity -pressure -force transform. The matriceal differential equation of wind induced vibratory state is dealt with by both, direct integration and modal decomposition. The three components of the mechanical state are expressed via base shear force -the static state, lateral story-level displacements -the kinematic state and wind induced energy -the energy state. Modal decomposition of the dynamic response allows for immediate computation of modal contribution to the total wind response. Computed values of the parameters are numerically and graphically presented and commented. Relevant conclusions are inferred.