  A cosmological model based on holographic scenarios is formulated in a flat
Friedmann-Robertson-Walker universe. To formulate this model, the cosmological
horizon is assumed to have a general entropy and a general temperature
(including Bekenstein-Hawking entropy and Gibbons-Hawking temperature,
respectively). In addition, a holographic-like connection [Eur. Phys. J. C 83,
690 (2023) (arXiv:2212.05822)] and Padmanabhan's holographic equipartition law
are assumed for the entropy and temperature, and the Friedmann and acceleration
equations are derived from these. The derived Friedmann and acceleration
equations include both the entropy and the temperature and are slightly
complicated, but can be combined into a single simple equation, corresponding
to a similar equation that describes the background evolution of the universe
in time-varying $\Lambda (t)$ cosmologies. The simple equation depends on the
entropy but not on the temperature because the temperatures in the Friedmann
and acceleration equations cancel each other. These results imply that the
holographic-like connection should be consistent with Padmanabhan's holographic
equipartition law through the present model and that the entropy plays a more
important role. When the Gibbons-Hawking temperature is used as the
temperature, the Friedmann and acceleration equations are found to be
equivalent to those for a $\Lambda(t)$ model. A particular case of the present
model is also examined, applying a power-law corrected entropy.
