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Inequalities appear in various fields of natural science and engineering. Classical inequalities are still being improved and/or generalized by many researchers. That is, inequalities have been actively studied by mathematicians. In this book, we selected the papers that were published as the Special Issue ‘’Inequalities’’ in the journal Mathematics (MDPI publisher). They were ordered by similar topics for readers’ convenience and to give new and interesting results in mathematical inequalities, such as the improvements in famous inequalities, the results of Frame theory, the coefficient inequalities of functions, and the kind of convex functions used for Hermite–Hadamard inequalities. The editor believes that the contents of this book will be useful to study the latest results for researchers of this field.

quantum estimates --- Montgomery identity --- power inequalities --- positive linear map --- Hilbert C*-module --- Hermite–Hadamard type inequality --- Steffensen’s inequality --- Hilbert space --- Hadamard fractional integrals --- K-dual --- adjointable operator --- analytic functions --- special means --- geometrically convex function --- h2)-convex --- proportional fractional derivative --- commutator --- quasi-convex --- Katugampola fractional integrals --- Euler-Maclaurin summation formula --- starlike functions --- strongly ?-convex functions --- g-frame --- interval-valued functions --- twice differentiable convex functions --- Taylor theorem --- exponential inequalities --- g-Bessel sequence --- Riemann–Liouville and Caputo proportional fractional initial value problem --- frame --- Fejér’s inequality --- weight function --- Hermite-Hadamard type inequalities --- Gronwall–Bellman inequality --- ?-variation --- Hölder’s inequality --- majorization inequality --- alternate dual frame --- half-discrete Hardy-Hilbert’s inequality --- parameter --- Power mean inequality --- Riemann–Liouville fractional integrals --- reverse inequality --- weaving frame operator --- Fink’s identity --- pseudo-inverse --- operator inequality --- Hermite-Hadamard inequality --- one-sided weighted Morrey space --- Green functions --- weaving K-frame --- operator Kantorovich inequality --- higher order convexity --- weaving frame --- (h1 --- one-sided weighted Campanato space --- Fekete-Szegö inequality --- convex functions --- refined inequality --- trigonometric inequalities --- one-sided singular integral