BACKGROUND Athletes are expected to consider multiple factors when making informed decision about nutritional supplement use. Besides rules, regulations and potential health hazards, the efficacy of different nutritional supplements in performance enhancement is a key issue. The aim of this paper was to find evidence for informed decision making by investigating the relationship between specifi...

In this paper we prove a new version of Kransoselskii's fixed-point theorem under ($\psi, \theta, \varphi$)-weak contraction condition. The theoretical result is applied to the existence solution following fractional hybrid differential equation involving Riemann-Liouville and integral operators orders $0<\alpha<1$ $\beta>0:$ \begin{equation}\nonumber \left\{\begin{array}{ll} D^{\alpha}[x(t)-f(...

A bounded linear operator T on a Hilbert space is said to be homogeneous if $$\varphi (T)$$ unitarily equivalent for all $$ in the group Möb of bi-holomorphic automorphisms unit disc. projective unitary representation $$\sigma associated with an (T)= \sigma (\varphi )^* )$$ Möb. In this paper, we develop Möbius equivariant version Sz.-Nagy–Foias model theory completely non-unitary (cnu) contrac...