Refinements and sharpenings of some double inequalities for bounding the gamma function.
Refinements, generalizations, and applications of Jordan's inequality and related problems.
Refinements of Carleman's inequality.
Refinements of inequalities between the sum of squares and the exponential of sum of a nonnegative sequence.
Refinements of results about weighted mixed symmetric means and related Cauchy means.
Refinements of reverse triangle inequalities in inner product spaces.
Refinements of the Hermite-Hadamard inequality for convex functions.
Refining the Hölder and Minkowski inequalities.
Regarding arc-wise accessibility in the plane
Regular fractional iteration of convex functions
The existence of a unique solution φ of equation (1) is proved under the condition that f: I → I is convex or concave and of class in I, 0 < f(x) < x in I*, and f’(x) > 0 in I. Here I = [0, a] or [0, a), 0 < a ≤ ∞, and I* = I 0.
Regular fractional iterations.
Regular Iteration in the Case of Multiplier Zero
Regular mappings between dimensions
The notions of Lipschitz and bilipschitz mappings provide classes of mappings connected to the geometry of metric spaces in certain ways. A notion between these two is given by regular mappings (reviewed in Section 1), in which some non-bilipschitz behavior is allowed, but with limitations on this, and in a quantitative way. In this paper we look at a class of mappings called (s, t)-regular mappings. These mappings are the same as ordinary regular mappings when s = t, but otherwise they behave somewhat...
Regular Variation In Probability Theory
Regular variation on homogeneous cones
Régularité Gevrey au sens de Beurling ou Roumieu pour l'opérateur ... dans des ouverts non bornés.
Regularity, nonoscillation and asymptotic behaviour of solutions of second order linear equations.
Regularity of convex functions on Heisenberg groups
We discuss differentiability properties of convex functions on Heisenberg groups. We show that the notions of horizontal convexity (h-convexity) and viscosity convexity (v-convexity) are equivalent and that h-convex functions are locally Lipschitz continuous. Finally we exhibit Weierstrass-type h-convex functions which are nowhere differentiable in the vertical direction on a dense set or on a Cantor set of vertical lines.
Regularity of Lipschitz minima
Regularity of the Hardy-Littlewood maximal operator on block decreasing functions
We study the Hardy-Littlewood maximal operator defined via an unconditional norm, acting on block decreasing functions. We show that the uncentered maximal operator maps block decreasing functions of special bounded variation to functions with integrable distributional derivatives, thus improving their regularity. In the special case of the maximal operator defined by the -norm, that is, by averaging over cubes, the result extends to block decreasing functions of bounded variation, not necessarily...