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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

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This Special Issue brings together original research papers, in all areas of mathematics, that are concerned with inequalities or the role of inequalities. The research results presented in this Special Issue are related to improvements in classical inequalities, highlighting their applications and promoting an exchange of ideas between mathematicians from many parts of the world dedicated to the theory of inequalities. This volume will be of interest to mathematicians specializing in inequality theory and beyond. Many of the studies presented here can be very useful in demonstrating new results. It is our great pleasure to publish this book. All contents were peer-reviewed by multiple referees and published as papers in our Special Issue in the journal Symmetry. These studies give new and interesting results in mathematical inequalities enabling readers to obtain the latest developments in the fields of mathematical inequalities. Finally, we would like to thank all the authors who have published their valuable work in this Special Issue. We would also like to thank the editors of the journal Symmetry for their help in making this volume, especially Mrs. Teresa Yu.

Research & information: general --- Geography --- Ostrowski inequality --- Hölder's inequality --- power mean integral inequality --- n-polynomial exponentially s-convex function --- weight coefficient --- Euler-Maclaurin summation formula --- Abel's partial summation formula --- half-discrete Hilbert-type inequality --- upper limit function --- Hermite-Hadamard inequality --- (p, q)-calculus --- convex functions --- trapezoid-type inequality --- fractional integrals --- functions of bounded variations --- (p,q)-integral --- post quantum calculus --- convex function --- a priori bounds --- 2D primitive equations --- continuous dependence --- heat source --- Jensen functional --- A-G-H inequalities --- global bounds --- power means --- Simpson-type inequalities --- thermoelastic plate --- Phragmén-Lindelöf alternative --- Saint-Venant principle --- biharmonic equation --- symmetric function --- Schur-convexity --- inequality --- special means --- Shannon entropy --- Tsallis entropy --- Fermi-Dirac entropy --- Bose-Einstein entropy --- arithmetic mean --- geometric mean --- Young's inequality --- Simpson's inequalities --- post-quantum calculus --- spatial decay estimates --- Brinkman equations --- midpoint and trapezoidal inequality --- Simpson's inequality --- harmonically convex functions --- Simpson inequality --- (n,m)-generalized convexity --- Ostrowski inequality --- Hölder's inequality --- power mean integral inequality --- n-polynomial exponentially s-convex function --- weight coefficient --- Euler-Maclaurin summation formula --- Abel's partial summation formula --- half-discrete Hilbert-type inequality --- upper limit function --- Hermite-Hadamard inequality --- (p, q)-calculus --- convex functions --- trapezoid-type inequality --- fractional integrals --- functions of bounded variations --- (p,q)-integral --- post quantum calculus --- convex function --- a priori bounds --- 2D primitive equations --- continuous dependence --- heat source --- Jensen functional --- A-G-H inequalities --- global bounds --- power means --- Simpson-type inequalities --- thermoelastic plate --- Phragmén-Lindelöf alternative --- Saint-Venant principle --- biharmonic equation --- symmetric function --- Schur-convexity --- inequality --- special means --- Shannon entropy --- Tsallis entropy --- Fermi-Dirac entropy --- Bose-Einstein entropy --- arithmetic mean --- geometric mean --- Young's inequality --- Simpson's inequalities --- post-quantum calculus --- spatial decay estimates --- Brinkman equations --- midpoint and trapezoidal inequality --- Simpson's inequality --- harmonically convex functions --- Simpson inequality --- (n,m)-generalized convexity

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