Generalized Jensen-Mercer inequality for functions with nondecreasing increments (Q1669238)

Summary: In [JIPAM, J. Inequal. Pure Appl. Math. 4, No. 4, Paper No. 73, 2 p. (2003; Zbl 1048.26016)], \textit{A. McD. Mercer} established an interesting variation of Jensen's inequality and later in 2009 Mercer's result was generalized to higher dimensions by \textit{M. Niezgoda} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 7--8, 2771--2779 (2009; Zbl 1177.26016)]. Recently, Asif et al. has stated an integral version of Niezgoda's result for convex functions. We further generalize Niezgoda's integral result for functions with nondecreasing increments and give some refinements with applications. In the way, we generalize an important result, Jensen-Boas inequality, using functions with nondecreasing increments. These results would constitute a valuable addition to Jensen-type inequalities in the literature.