Different types of quantum integral inequalities via ( α , m ) -convexity.

In this paper, based on ( α , m ) -convexity, we establish different type inequalities via quantum integrals. These inequalities generalize some results given in the literature.

Extensions of different type parameterized inequalities for generalized [Formula: see text]-preinvex mappings via k-fractional integrals.

The authors discover a general k-fractional integral identity with multi-parameters for twice differentiable functions. By using this integral equation, the authors derive some new bounds on Hermite-Hadamard's and Simpson's inequalities for generalized [Formula: see text]-preinvex functions through k-fractional integrals. By taking the special parameter values for various suitable choices of function h, some interesting results are also obtained.

Certain new bounds considering the weighted Simpson-like type inequality and applications.

We investigate a weighted Simpson-type identity and obtain new estimation-type results related to the weighted Simpson-like type inequality for the first-order differentiable mappings. We also present some applications to f-divergence measures and to higher moments of continuous random variables.