We propose a local method of constructing piecewise G Bézier patches to span an irregular curve network, without modifying the given curves at oddand 4-valent node points. Topologically irregular regions of the network are approximated by implicit surfaces, which are used to generate split curves, which subdivide the regions into triangular and/or rectangular sub-regions. The subdivided regions...

A Cayley map is a 2-cell embedding of a Cayley graph into an orientable surface with the same local orientation induced by a cyclic permutation of generators at each vertex. In this paper, we provide classifications of prime-valent regular Cayley maps on abelian groups, dihedral groups and dicyclic groups. Consequently, we show that all prime-valent regular Cayley maps on dihedral groups are ba...

The purpose of this paper is to derive some subordination and superordination results for functions of the form f(z) = zp + ∞ ∑ k=p+1 akz k which are p−valent in the open unit disk U = {z ∈ C : |z| < 1} by using certain differential operator Aλ,p(α, β, μ)f(z) and integral operator F m p (ρ, θ)f(z). Some special cases are also considered.

This paper investigates various new subordination results for certain p -valent analytic functions involving a generalized multiplier transformation operator Jm p (λ , l),m ∈ Z, defined recently by J. K. Prajapat [Math. Comput. Modelling, 55 (2012), 1456–1465]. Several lines of approach are followed to obtain the subordination results. We also consider some simpler and precise forms of the deri...

A construction is given of a valent arc transitive graph with vertex stabilizer isomorphic to the dihedral group D The graph has vertices and is the rst known example of a valent arc transitive graph with nonabelian vertex stabilizer A VALENT HALF ARC TRANSITIVE GRAPH

Department of Mathematics and Astronomy University of Lucknow, Lucknow 226007, India sharma [email protected] pathakmamta [email protected] Abstract In this paper, a necessary and sufficient condition for a function to be in the class Tμ(α, p,A,B) of p-valent analytic functions involving fractional calculus operator is obtained. Distortion bounds, subordination result, convolution results ...

Abstract. In this paper, we introduce and investigate the various properties and characteristics of the classMa,c(p;β;A,B) and its subclassM + a,c(p; β;A,B) of meromorphically p-valent functions of order β(pβ > 1), which are defined by means of the Liu-Srivastava operator. In particular, several inclusion relations, coefficients estimates, distortion theorems ,neighborhoods partial, Hadamard pr...

For certain meromorphic p-valent functioun φ andψ, we study a class of functioun f (z) = 1 zp + ∑∞ n=p anz n, (an ≥ 0), defined in the punctured unit disc D, satisfying R ( (f∗φ)(z) (f∗ψ)(z) ) > α (0 ≤ α ≤ 1, z ∈ D) . Coeffiicient etimate disortion theorem and radii of starlikeness and convexity are obtained. Further we consider integral operators associated with functions belonging to the afor...

For a given p-valent analytic function g with positive coefficients in the open unit disk ∆, we study a class of functions f(z) = z + ∑∞ n=m anz , an ≥ 0 satisfying 1 p < ( z(f ∗ g)′(z) (f ∗ g)(z) ) < α ( z ∈ ∆; 1 < α < m+ p 2p ) . Coefficient inequalities, distortion and covering theorems, as well as closure theorems are determined. The results obtained extend several known results as special ...

The projection on the base plane of a regular minimal surface S in R with isothermal parameters defines a complex-valued univalent harmonic function f = h(z) + g(z). The aim of this paper is to obtain the distortion inequalities for the Weierstrass-Enneper parameters of the minimal surface for the harmonic multivalent functions for which analytic part is an m-valent convex function. 2000 Mathem...