  The present work is a generalization of the recent work [arXiv: 1206.1420] on
the modified Hawking temperature on the event horizon. Here the Hawking
temperature is generalized by multiplying the modified Hawking temperature by a
variable parameter \alpha representing the ratio of the growth rate of the
apparent horizon to the event horizon. It is found that both the first and the
generalized second law of thermodynamics are valid on the event horizon for any
fluid distribution. Subsequently, Bekenstein entropy is modified on the event
horizon and thermodynamical laws are examined. Finally, interpretation of the
parameters involved has been presented.
