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In this work, we prove Ostrowski–Mercer inequalities for differentiable harmonically convex functions. It is also shown that the newly proved inequalities can be converted into some existing inequalities. Furthermore, it is provided that how the newly discovered inequalities can be applied to special means of real numbers. [ABSTRACT FROM AUTHOR]

This paper concentrates on the error estimation of novel time second‐order splitting conservative finite difference method (FDM) for high‐dimensional nonlinear fractional Schrödinger equation rigorously. The discrete preservation property of our scheme is exhibited. By virtue of the cut‐off technique and discrete energy method, it is shown that our scheme possesses the accuracy of O(Δt2+hx2+hy2) in sense of L2‐ norm. Numerical experiments are exhibited to validate the accuracy and conservation property of our scheme. [ABSTRACT FROM AUTHOR]

In this paper, we prove two identities involving quantum derivatives, quantum integrals, and certain parameters. Using the newly proved identities, we prove new inequalities of Simpson's and Newton's type for quantum differentiable convex functions under certain assumptions. Moreover, we discuss the special cases of our main results and obtain some new and existing Simpson's type inequalities, Newton's type inequalities, midpoint type inequalities, and trapezoidal type inequalities. [ABSTRACT FROM AUTHOR]

In this study, we established some new inequalities of Ostrowski type for the functions of two variables by using the concept of newly defined double quantum integrals. We also revealed that the results presented in this paper are the consolidation and generalization of some existing results on the literature of Ostrowski inequalities. [ABSTRACT FROM AUTHOR]

In this article, by using the notion of newly defined q1q2 derivatives and integrals, some new Simpson's type inequalities for coordinated convex functions are proved. The outcomes raised in this paper are extensions and generalizations of the comparable results in the literature on Simpson's inequalities for coordinated convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals. [ABSTRACT FROM AUTHOR]

We first establish two new identities, based on the kernel functions with either two section or three sections, involving quantum integrals by using new definition of quantum derivative. Then, some new inequalities related to Simpson's 1/3 formula for convex mappings are provided. In addition, Newton type inequalities, for functions whose quantum derivatives in modulus or their powers are convex, are deduced. We also mention that the results in this work generalize inequalities given in earlier study. [ABSTRACT FROM AUTHOR]