Extension of functions satisfying lipschitz conditions

Extension of P-adic Definable Lipschitz Functions

Write OK for the valuation ting, MK for the maximal ideal of K and kK for the residue field. Let us fix $ some uniformizer of K. We denote by acm : K → OK/(MK) the map sending some nonzero x ∈ K to x$−ord(x) mod MK , and sending zero to zero. This is a definable map. We denote by RV the union of K×/(1 +MK) and {0} and by rv : K → RV the quotient map. More generally, if m ∈ N∗, we set RVm = K×/(...

On the Extension of Lipschitz, Lipschitz- Hölder Continuous, and Monotone Functions

Complete characterization of functions satisfying the conditions of Arrow's theorem

Arrow’s theorem implies that a social welfare function satisfying Transitivity, the Weak Pareto Principle (Unanimity) and Independence of Irrelevant Alternatives (IIA) must be dictatorial. When non-strict preferences are also allowed, a dictatorial social welfare function is defined as a function for which there exists a single voter whose strict preferences are followed. This definition allows...

Certain Subclasses of Bi–univalent Functions Satisfying Subordinate Conditions

In this paper, we introduce and investigate each of the following subclasses: SΣ(λ ,γ ;φ), H S Σ(α), RΣ(η ,γ ;φ) and BΣ(μ ;φ) (0 λ 1; γ ∈ C {0}; α ∈ C; 0 η < 1; μ 0) of bi-univalent functions, φ is an analytic function with positive real part in the unit disk D, satisfying φ(0) = 1, φ ′(0) > 0, and φ(D) is symmetric with respect to the real axis. We obtain coefficient bounds involving the Taylo...

The Fekete-Szegö problem for a general class of bi-univalent functions satisfying subordinate conditions

In this work, we obtain the Fekete-Szegö inequalities for the class $P_{Sigma }left( lambda ,phi right) $ of bi-univalent functions. The results presented in this paper improve the recent work of Prema and Keerthi [11].