In this paper, we introduce a new subclass of harmonic functions f = s + ¯ t f=s+t¯ in the open unit disk U { z ∈ C : | < 1 } U={z∈C:|z|<1} satisfying ${\text{Re}}\left[ \gamma \mathfrak{s}^{\prime }(z)+\delta z\mathfrak{s}^{\prime \prime }(z)+\left( \frac{\delta -\gamma }{2}\right) z^{2}\mathfrak{s}^{\prime }\left( z\right) -\lambda \right]>\left \vert \mathfrak{t}^{\prime z\mathfrak{t}^{\prim...

This paper studies the relation between convexity of TU games and marginal vectors. Shapley (1971) andIchiishi (1981) showed that a game is convex if and only if all marginal vectors are core elements. In Rafels,Ybern (1995) it is shown that if all even marginal vectors are core elements, then all odd marginal vectorsare core elements as well, and vice versa. Hence, if all even or a...

In this paper, we introduce a new convexity on graphs similar to the well known P3convexity [3], which we will call P ∗ 3 -convexity. We show that several P ∗ 3 -convexity parameters (hull number, convexity number, Carathéodory number, Radon number, interval number and percolation time) are NP-hard even on bipartite graphs. We show a strong relation between this convexity and the well known geo...

The aim of this paper is to present a general approach to the problem of shape preserving interpolation. The problem of convexity preserving interpolation using C Hermite splines with one free generating function is considered.

Necessary conditions for Pareto optimality in multiobjective programming with subdifferentiable set functions are established in Theorem 12 of H. C. Lai and L. J. Ž . Lin J. Math. Anal. Appl. 132, 1988, 558]571 . In this paper, we establish some sufficient conditions under which a feasible solution of such a problem will be Pareto optimal provided that a weaker convexity requirement is satisfie...

In this paper, we present a technique for grouping line segments sinto convex sets, where the line segments are obtained by linking edges obtained from the Canny edge detector. The novelty of the approach is twofold: rst we de ne an e cient approach for testing the global convexity criterion, and second, we develop an optimal search based on dynamic programming or grouping the line segments int...

In this paper, the Schur convexity is generalized to Schur f -convexity, which contains the Schur geometrical convexity, harmonic convexity and so on. When f : R+ →R is defined by f (x) = (xm−1)/m if m = 0 and f (x) = lnx if m = 0 , the necessary and sufficient conditions for f -convexity (is called Schur m -power convexity) of Daróczy means are given, which improve, generalize and unify Shi et...

the object of this paper to derive certain sucient condi-tions for close-to-convexity of certain analytic functions dened on theunit disk

An upper bound q(c) for the best, under equivalent renorming, possible power type of the modulus of smoothness of a Banach space with modulus of convexity satisfying δX(ε) cε2, is found. The estimate is asymptotically sharp and is expressed in terms of linear fractional function q(c). © 2006 Elsevier Inc. All rights reserved.