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In this paper, we consider the class of generalized quasi-convex. Then using this convexity, we obtain some new generalized Hermite-Hadamard type integral inequalities for the generalized quasi-convex functions.

In this paper, we establish the generalized Ostrowski type inequality involving local fractional integrals on fractal sets RÎ±(0 < Î± â‰¤ 1) of real line numbers. Some applications for special means of fractal sets RÎ± are also given. The results presented here would provide extensions of those given in earlier works.

In this study, we establish generalized Gruss type inequality and some generalized ?ebysev type inequalities for local fractional integrals on fractal sets RÎ± (0 <Î± ? 1) of real line numbers.

First of all, the generalized Pompeiu's mean value theorem is established. Then, some generalized Pompeiu type inequalities are obtained. Finally, some applications of these inequalities in numerical integration and for special means are given.

Inequalities of Hermiteâ€“Hadamard type for functions whose derivatives in absolute value are convex with applications

Abstract In this paper some new Hadamard-type inequalities for functions whose derivatives in absolute values are convex are established. Some applications to special means of real numbers are given. Finally, we also give some applications of our obtained results to get new error bounds for the sum of the midpoint and trapezoidal formulae.

In the paper, two new identities involving the local fractional integrals have been established. Using these two identities, we obtain some generalized Hermite-Hadamard type integral inequalities for the local differentiable generalized convex functions.

We introduce the generalized convex function on fractal sets of real line numbers and study the properties of the generalized convex function. Based on these properties, we establish the generalized Jensenâ€™s inequality and generalized Hermite-Hadamard's inequality. Furthermore, some applications are given.

We introduce two kinds of generalized sconvex functions on real linear fractal sets \mathbb{R}^{\alpha}(0<\alpha<1) And similar to the class situation, we also study the properties of these two kinds of generalized sconvex functions and discuss the relationship between them. Furthermore, some applications are given.

The fractal wave equations with local fractional derivatives are investigated in this paper. The analytical solutions are obtained by using local fractional Fourier series method. The present method is very efficient and accurate to process a class of local fractional differential equations.

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