Abstract
It is always attractive and motivating to acquire the generalizations of known results. In this article, we introduce a new class C(h) of functions which can be represented in a form of integral transforms involving general kernel with sigma -finite measure. We obtain some new Polya-Szego and ebyev type inequalities as generalizations to the previously proved ones for different fractional integrals including fractional integral of a function with respect to another function capturing Riemann-Liouville integrals, Hadamard fractional integrals, Katugampola fractional integral operators, and conformable fractional integrals. This new idea shall motivate the researchers to prove the results over a measure space with general kernels instead of special kernels.