On linear estimates defined by a continuous weight function

Approximating optimal paths in terrains with weight defined by a piecewise-linear function

Finding optimal paths in non-homogeneous terrains is a class of problem that presents itself in many situations. One of the best-known versions is the so-called Weighted Region Problem (WRP) [2],[3],[4],[5], based on a model of space with regions of constant weight. Here this version is generalized using linear functions defined to coincide with the weights assigned at the vertices of a patchwo...

On a linear combination of classes of harmonic $p-$valent functions defined by certain modified operator

In this paper we obtain coefficient characterization‎, ‎extreme points and‎ ‎distortion bounds for the classes of harmonic $p-$valent functions‎ ‎defined by certain modified operator‎. ‎Some of our results improve‎ ‎and generalize previously known results‎.

On Sequences Defined by Linear

where a, ai, a2> ■ ■ ■ , a* are given rational integers. The purpose of this paper is to investigate the periodicity of such sequences with respect to a rational integral modulus m. Carmichaelî has studied the period for a modulus m whose prime divisors exceed k and are prime to ak. In this paper, I give a solution to the problem without restriction on m. If m is prime to ak the sequence (1) is...

Faber polynomial coefficient estimates for bi-univalent functions defined by subordinations

A function is said to be bi-univalent on the open unit disk D if both the function and its inverse are univalent in D. Not much is known about the behavior of the classes of bi-univalent functions let alone about their coefficients. In this paper we use the Faber polynomial expansions to find coefficient estimates for four well-known classes of bi-univalent functions which are defined by subord...

Univalence of Certain Linear Operators Defined by Hypergeometric Function