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In this paper, we aim at establishing an analog of the recently published results [1] with the help of new k− type fractional integral operator Rω [ f ](t) , which is introduced here by using the ω -weighted classes. Then we establish some new ω -weighted Pólya-Szegö type integral inequalities and ω -weighted fractional integral inequalities, which are the an analog of the recently published results [1]. Mathematics subject classification (2010): 26D10, 26A33, 26D15.

An extension by means of ω-weighted classes of the generalized Riemann-Liouville k-fractional integral inequalities