On Iyengar-type inequalities via quasi-convexity and quasi-concavity

Quasi-convexity and Shrinkwrapping

We extend a result of Minsky to show that for a map of a surface to a hyperbolic 3-manifold which is not necessarily π1-injective but is 2-incompressible rel a geodesic link with a definite tube radius, the set of noncontractible simple loops with a bounded length representatives is quasi-convex in the complex of curves.

Quasi-convexity, strictly quasi-convexity and pseudo-convexity of composite objective functions

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Lebesgue-type Inequalities for Quasi-greedy Bases

(m1,m2)-Convexity and Some New Hermite-Hadamard Type Inequalities

In this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Hölder-İşcan inequality gives a better approach than...

Lebesgue-type Inequalities for Quasi-greedy Bases

We show that for quasi-greedy bases in real or complex Banach spaces the error of the thresholding greedy algorithm of order N is bounded by the best N term error of approximation times a function of N which depends on the democracy functions and the quasi-greedy constant of the basis. If the basis is democratic this function is bounded by C logN . We show with two examples that this bound is a...