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This book presents the recent developments in the field of geometric inequalities and their applications. The volume covers a vast range of topics, such as complex geometry, contact geometry, statistical manifolds, Riemannian submanifolds, optimization theory, topology of manifolds, log-concave functions, Obata differential equation, Chen invariants, Einstein spaces, warped products, solitons, isoperimetric problem, Erdös–Mordell inequality, Barrow’s inequality, Simpson inequality, Chen inequalities, and q-integral inequalities. By exposing new concepts, techniques and ideas, this book will certainly stimulate further research in the field.

Erdös–Mordell inequality --- Barrow’s inequality --- triangle --- interior point --- q-integral inequality --- strongly preinvex function --- Simpson inequality --- quantum integral --- statistical warped product submanifold --- statistical manifold --- B.Y.Chen inequality --- Casorati curvatures --- statistical soliton --- Wintgen inequality --- generalized complex space form --- generalized Sasakian space form --- Lagrangian submanifold --- Legendrian submanifold --- Einstein manifold --- sectional curvature --- Betti number --- Tachibana number --- spherical space form --- slant submanifolds --- generalized Sasakian space forms --- closed form --- conformal form --- Maslov form --- legendrian submanifolds --- sasakian space forms --- obata differential equation --- isometric immersion --- Casorati curvature --- statistical submanifold --- holomorphic statistical manifold --- clifford minimal hypersurfaces --- sasakian structure --- integral inequalities --- reeb function --- contact vector field --- δ(2,2)-invariant --- Chen inequalities --- Lagrangian submanifolds --- quaternionic space forms --- complex space forms --- warped product --- sphere theorem --- Laplacian --- inequalities --- diffeomorphic --- Ricci curvature --- skew CR-warped product submanifolds --- complex space form --- CR-warped product submanifolds --- semi slant warped product submanifolds --- almost Hermitian manifolds --- Kähler identities --- Lefschetz operator --- isoperimetric problem --- minimal perimeter --- log-concave functions --- isotropic measure --- extrinsic principal tangential directions --- principal first normal directions

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book presents the recent developments in the field of geometric inequalities and their applications. The volume covers a vast range of topics, such as complex geometry, contact geometry, statistical manifolds, Riemannian submanifolds, optimization theory, topology of manifolds, log-concave functions, Obata differential equation, Chen invariants, Einstein spaces, warped products, solitons, isoperimetric problem, Erdös–Mordell inequality, Barrow’s inequality, Simpson inequality, Chen inequalities, and q-integral inequalities. By exposing new concepts, techniques and ideas, this book will certainly stimulate further research in the field.

Research & information: general --- Mathematics & science --- Erdös–Mordell inequality --- Barrow’s inequality --- triangle --- interior point --- q-integral inequality --- strongly preinvex function --- Simpson inequality --- quantum integral --- statistical warped product submanifold --- statistical manifold --- B.Y.Chen inequality --- Casorati curvatures --- statistical soliton --- Wintgen inequality --- generalized complex space form --- generalized Sasakian space form --- Lagrangian submanifold --- Legendrian submanifold --- Einstein manifold --- sectional curvature --- Betti number --- Tachibana number --- spherical space form --- slant submanifolds --- generalized Sasakian space forms --- closed form --- conformal form --- Maslov form --- legendrian submanifolds --- sasakian space forms --- obata differential equation --- isometric immersion --- Casorati curvature --- statistical submanifold --- holomorphic statistical manifold --- clifford minimal hypersurfaces --- sasakian structure --- integral inequalities --- reeb function --- contact vector field --- δ(2,2)-invariant --- Chen inequalities --- Lagrangian submanifolds --- quaternionic space forms --- complex space forms --- warped product --- sphere theorem --- Laplacian --- inequalities --- diffeomorphic --- Ricci curvature --- skew CR-warped product submanifolds --- complex space form --- CR-warped product submanifolds --- semi slant warped product submanifolds --- almost Hermitian manifolds --- Kähler identities --- Lefschetz operator --- isoperimetric problem --- minimal perimeter --- log-concave functions --- isotropic measure --- extrinsic principal tangential directions --- principal first normal directions --- Erdös–Mordell inequality --- Barrow’s inequality --- triangle --- interior point --- q-integral inequality --- strongly preinvex function --- Simpson inequality --- quantum integral --- statistical warped product submanifold --- statistical manifold --- B.Y.Chen inequality --- Casorati curvatures --- statistical soliton --- Wintgen inequality --- generalized complex space form --- generalized Sasakian space form --- Lagrangian submanifold --- Legendrian submanifold --- Einstein manifold --- sectional curvature --- Betti number --- Tachibana number --- spherical space form --- slant submanifolds --- generalized Sasakian space forms --- closed form --- conformal form --- Maslov form --- legendrian submanifolds --- sasakian space forms --- obata differential equation --- isometric immersion --- Casorati curvature --- statistical submanifold --- holomorphic statistical manifold --- clifford minimal hypersurfaces --- sasakian structure --- integral inequalities --- reeb function --- contact vector field --- δ(2,2)-invariant --- Chen inequalities --- Lagrangian submanifolds --- quaternionic space forms --- complex space forms --- warped product --- sphere theorem --- Laplacian --- inequalities --- diffeomorphic --- Ricci curvature --- skew CR-warped product submanifolds --- complex space form --- CR-warped product submanifolds --- semi slant warped product submanifolds --- almost Hermitian manifolds --- Kähler identities --- Lefschetz operator --- isoperimetric problem --- minimal perimeter --- log-concave functions --- isotropic measure --- extrinsic principal tangential directions --- principal first normal directions

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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.

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 --- n/a --- Hölder's inequality --- Euler-Maclaurin summation formula --- Abel's partial summation formula --- Hermite-Hadamard inequality --- Phragmén-Lindelöf alternative --- Fermi-Dirac entropy --- Bose-Einstein entropy --- Young's inequality --- Simpson's inequalities --- Simpson's inequality --- (n,m)-generalized convexity