No abstract

In this work, the concepts of quantum derivative and quantum integral are renamed to be the left quantum derivative and the left de.. . nite quantum integral. Symmetrically to the left, a new quantum derivative (the right) and de.. . nite quantum integral (the right) are de.. . ned. Some properties of these new concepts are investigated and as well as according todo these new concepts some inaccuracies in quantum integral inequalities are corrected. Moreover, some new quantum Hermite-Hadamard type inequalities are established. Hosted file M_Kunt_, A_ W_ Baidar_and_Z_\selectlanguage{polish}Ş\selectlanguage{english}anl\selectlanguage{polish}ı.

In this work, new quantum derivative and integral concepts are de…ned. Some properties of these new concepts are investigated. Using two symmetrically quantum integrals together, some new quantum Hermite-Hadamard type inequalities are established. Also, using a new quantum identity, some known trapezoid type inequalities are extended to quantum analogs.

In this paper, we present a new generalized class of harmonically convex functions and discuss some of their algebraic properties. Furthermore, we establish some Hermite–Hadamard‐type inequalities via new generalized harmonically convexity. As applications of the findings in this study, some particular cases are described.

In this paper a new quantum analog of Hermite-Hadamard inequality is presented, and based on it, two new quantum trapezoid and midpoint identities are obtained. Moreover, the quantum analog of some trapezoid and midpoint type inequalities are established.