Using the notion of eta-convex functions as generalization of convex functions, we estimate the difference between the middle and right terms in Hermite-Hadamard-Fejer inequality for differentiable mappings. Also as an application we give an error estimate for midpoint formula.

Recently, there has been a strong push toward creating and expanding quadrature inequalities in quantum calculus. In order to investigate various avenues for inquiry, number of extensions midpoint estimations are studied. The goal this research article is discover novel midpoint-type that twice q?2-differentiable (?,m)-convex functions. Firstly, we obtain identity q?2-integral by employing calc...

In this paper‎, ‎making use of a new identity‎, ‎we establish new‎ ‎inequalities of Ostrowski type for the class of preinvex functions and‎ ‎gave some midpoint type inequalities‎.

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In this work, we suggest a general viscosity implicit midpoint rule for nonexpansive mapping in the framework of Hilbert space. Further, under certain conditions imposed on sequence parameters, strong convergence theorem is proved by generated proposed iterative scheme, which, addition, unique solution variational inequality problem. Furthermore, provide some applications to inequalities, Fredh...