Faiza Rubab - Department of Mathematics, University of Karachi, University Road, Karachi-۷۵۲۷۰ Pakistan.
Asif Khan - Department of Mathematics, University of Karachi, University Road, Karachi-۷۵۲۷۰ Pakistan.
Anum Naqvi - Department of Basic Sciences, Muhammad Ali Jinnah University, P.E.C.H.S. Main Shahrah-e-Faisal, Karachi-۷۵۴۰۰, Pakistan.
Ani Haider - Department of Mathematics, University of Karachi, University Road, Karachi-۷۵۲۷۰ Pakistan.

Motivated by the results of Niezgoda, corresponding to the generalization of Mercer's inequality for positive weights, in this paper, we consider real weights, for which we establish related results. To be more specific, Niezgoda's results are derived under Jensen Steffensen conditions. In addition, we construct some functionals enabling us to refine Niezgoda's results. Lastly, we discuss some applications.

Jensen-Mercer inequality, Jensen-Steffensen inequality, Majorization theorem, Subdifferential