Applications of one- and two-dimensional Volterra inequalities in differential equations of the hyperbolic type.
Applications of P-adic generalized functions and approximations by a system of P-adic translations of a function.
Applications of the extended Hermite-Hadamard inequality.
Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions
2000 Mathematics Subject Classification: Primary 30C45, 26A33; Secondary 33C15By making use of the fractional differential operator Ω^λz (0 ≤ λ < 1) due to Owa and Srivastava, a new subclass of univalent functions denoted by k−SPλ (0 ≤ k < ∞) is introduced. The class k−SPλ unifies the concepts of k-uniformly convex functions and k-starlike functions. Certain basic properties of k − SPλ such as inclusion theorem, subordination theorem, growth theorem and class preserving transforms are studied.*...
Applications of the Rådström-Hörmander Embedding Theorem to Multifunctions
Using the Rådström-Hörmander theorem on embedding of the hyperspace of closed convex sets in a Banach space, we prove multivalued versions of some results known for real functions.
Applications of ultrapowers to the uniform and Lipschitz classification of Banach spaces
Approaching the power logarithmic and difference means by iterative algorithms involving the power binomial mean.
Approximate and Peano derivatives of nonintegral order
Let n be a nonnegative integer and let u ∈ (n,n+1]. We say that f is u-times Peano bounded in the approximate (resp. , 1 ≤ p ≤ ∞) sense at if there are numbers , |α| ≤ n, such that is in the approximate (resp. ) sense as h → 0. Suppose f is u-times Peano bounded in either the approximate or sense at each point of a bounded measurable set E. Then for every ε > 0 there is a perfect set Π ⊂ E and a smooth function g such that the Lebesgue measure of E∖Π is less than ε and f = g on Π....
Approximate derivatives and Baire classes
Approximate differentiation: Jarník points
Approximate maxima
Approximate of functions of two variables
Approximate smoothness of continuous functions
Approximate symmetric derivative and monotonicity
Approximately generalized convex functions.
Approximating real Pochhammer products: a comparison with powers
Accurate estimates of real Pochhammer products, lower (falling) and upper (rising), are presented. Double inequalities comparing the Pochhammer products with powers are given. Several examples showing how to use the established approximations are stated.
Approximating the finite Hilbert transform via an Ostrowski type inequality for functions of bounded variation.
Approximation of Lebesgue Integrals by Riemann Sums and Lattice Points in Domains with Fractal Boundary.
Approximation of Quasiconvex Functions, and Lower Semicontinuity of Multiple Integrals.
Approximation of set-valued functions with compact images-an overview
Continuous set-valued functions with convex images can be approximated by known positive operators of approximation, such as the Bernstein polynomial operators and the Schoenberg spline operators, with the usual sum between numbers replaced by the Minkowski sum of sets. Yet these operators fail to approximate set-valued functions with general sets as images. The Bernstein operators with growing degree, and the Schoenberg operators, when represented as spline subdivision schemes, converge to set-valued...