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1
Content available The extensive 1-median problem with radius on networks
Nhan Tran Hoai Ngoc, Hung Nguyen Thanh, Nguyen Kien Trung
Opuscula Mathematica
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2024
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Vol. 44, no. 1
135--149
EN
The median location problem concerns finding locations of one or several new facilities that minimize the overall weighted distances from the existing to the new facilities. We address the problem of locating one new facility with a radius r on networks. Furthermore, the radius r is flexible and the objective function is the conic combination of the traditional 1-median function and the value r. We call this problem an extensive 1-median problem with radius on networks. To solve the problem, we first induce the so-called finite dominating set, that contains all points on the underlying network and radius values which are candidate for the optimal solution of the problem. This helps to develop a combinatorial algorithm that solves the problem on a general network G = (V,E) in O(|E||V |3) time. We also consider the underlying problem with improved algorithm on trees. Based the convexity of the objective function with variable radius, we develop a linear time algorithm to find an extensive 1-median with radius on the underlying tree.
2
Content available remote A note on q-calculus
Ezeafulukwe U. A., Darus M.
Fasciculi Mathematici
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2015
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Nr 55
53--63
EN
In this article, we let PCq denote the class of q—convex functions. Certain analytic properties of the class PCq are studied. The maximum of the absolute value of the Fekete-Szegö functional is briefly determined.
3
Content available remote Subordination results and integral means inequalities for generalized k-starlike functions
Dziok J., Murugusundaramoorthy G., Wiśniowska W.
Journal of Mathematics and Applications
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2009
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Vol. 31
37-49
EN
In the paper, we introduce a generalized class of k-starlike functions associated with Wright generalized hypergeometric functions and obtain the sequential subordination results and integral means inequalities. Some interesting consequences of our results are also pointed out.
4
Content available remote Properties of a class of analytic functions involving a linear operator
Patel J., Sahoo P.
Demonstratio Mathematica
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2002
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Vol. 35, nr 3
495-507
5
Content available remote Integral representations of convex and concave set-valued functions
Piszczek M.
Demonstratio Mathematica
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2002
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Vol. 35, nr 4
727-742
EN
We will denote by C+ the family of all convex set-valued functions F denned on [a, b} with nonempty compact values, continuous at a, for which there exist all differences F(t) - F(s) as far as a < s < t < b. The main purpose oh this paper is to show that a function F belongs to the family C+ if and only if it is of the form t F(t)=F(a)+^\G(x)dx a for some decreasing set-valued function G.
6
Content available remote Classes of first-order differential superordinations
Bulboacă T.
Demonstratio Mathematica
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2002
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Vol. 35, nr 2
287-292
7
Content available remote On harmonic univalent mappings with small coefficients
Ganczar A.
Demonstratio Mathematica
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2001
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Vol. 34, nr 3
548-558
8
Content available remote A generalization of p-valent classes related to convex functions
Aouf M., Darwish H., Alhosseny A.
Demonstratio Mathematica
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2000
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Vol. 33, nr 3
467-479
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