On weighted exponential entropies

As an alternative to Shannon's classical entropy measure of information, an exponential entropy function was proposed by Pal and Pal in 1989 and 1991. To generalize Pal's entropy further, this author introduced two different families of exponential entropies that are one-parameter generalizations of Pal's entropy. The purpose of the present paper is to define weighted entropies corresponding to those one-parameter generalizations. Some properties and examples of such weighted exponential entropies are discussed.