A Lefschetz-type coincidence theorem for two maps f, g : X → Y from an arbitrary topological space to a manifold is given: Ifg = λfg , that is, the coincidence index is equal to the Lefschetz number. It follows that if λfg 6= 0 then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y...

Bent and plateaued functions play a significant role in cryptography since they can have various desirable cryptographic properties. In this work, we first provide the characterizations of plateaued functions in terms of the moments of their Walsh transforms. Next, we generalize the characterizations of Boolean bent and plateaued functions in terms of their second-order derivatives to arbitrary...

For λ ≥ 0 and 0 ≤ α < 1 < β, we denote by K (λ;α, β) the class of normalized analytic functions satisfying the two sided-inequality α << ( z f ′(z) f (z) + λ z2 f ′′(z) f (z) ) < β (z ∈ U), where U is the open unit disk. Let KΣ(λ;α, β) be the class of bi-univalent functions such that f and its inverse f −1 both belong to the class K (λ;α, β). In this paper, we establish bounds for the coefficie...

The present paper is divided into two parts. In the first part, we derive a Fan-KKM type theorem and establish some Fan type geometric properties of convex spaces. By applying our results, we also obtain some coincidence theorems and fixed-point theorems in the setting of convex spaces. The second part deals with the applications of our coincidence theorem to establish some existence results fo...

We first establish some existence results concerning approximate coincidence point properties and approximate fixed point properties for various types of nonlinear contractive maps in the setting of cone metric spaces and general metric spaces. From these results, we present some new coincidence point and fixed point theorems which generalize Berinde-Berinde’s fixed point theorem, Mizoguchi-Tak...

1. Introduction. Let Dbea bounded simply connected region of the complex z-plane which is regular for the Dirichlet problem, let C be the boundary of D, and let u be a continuous function on C to the real numbers. Some time ago J. L. Walsh [l, p. 517] suggested that it might be possible to define a sequence of harmonic polynomials by coincidence with the values of u in points so chosen on C tha...