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A generalization of the Mercer type inequality, for strongly convex functions with modulus c > 0, is hereby established. Let h : [δ, ζ] → R be a strongly convex function on the interval [δ, ζ] ⊂ R. Let a = (a1, ...., as), b = (b1, ...., bs) and p = (p1, ...., ps), where ak, bk ∈ [δ, ζ], pk > 0 for each k = 1, s. If n ∈ Rs, = 0 and under some separability assumptions, then we prove that s∑ l=1 plh(bl) ≤ s∑ l=1 plh(al) − c s∑ l=1, s(al − bl) ². Using the above result, we derive loads of inequalities for similarly separable vectors. We further applied our results to different types of tuples. Our results extend, complement and generalize known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we use the newly developed technique of parameter function to obtain some new Ostrowski type inequalities for double integrals. For this, we first obtain a generalized Montgomery identity for double integral and then use it obtain two Ostrowski type inequalities. Our results generalize some of the results of Zheng in [27] and Liu et al. in [22]. Furthermore, we apply our results to different time scales to obtain some interesting results that may be applied in the study of difference and differential equations. [ABSTRACT FROM AUTHOR]

Some trapezoid inequalities were proved in 2004 by B. G. Pach-patte. It is our purpose in this paper to extend these results to time scales. Besides that, two more results are also established. Furthermore, we also apply our results to continuous and discrete calculus to derive some new inequalities as special cases. [ABSTRACT FROM AUTHOR]