On exact triangle inequalities in (q1, q2)-quasimetric spaces

Tambov University Reports Series Natural and Technical Sciences ◽

10.20310/1810-0198-2019-24-125-33-38 ◽

2019 ◽

pp. 33-38

Author(s):

Zukhra Zhukovskaya ◽

Sergey Zhukovskiy ◽

Richik Sengupta

Keyword(s):

Triangle Inequality ◽

Continuous Functions ◽

Quasimetric Space ◽

Exact Triangle

For arbitrary (q1, q2) -quasimetric space, it is proved that there exists a function f, such that f -triangle inequality is more exact than any (q1, q2) -triangle inequality. It is shown that this function f is the least one in the set of all concave continuous functions g for which g -triangle inequality hold.

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Similarity, separability, and the triangle inequality.

Psychological Review ◽

10.1037/0033-295x.89.2.123 ◽

1982 ◽

Vol 89 (2) ◽

pp. 123-154 ◽

Cited By ~ 236

Author(s):

Amos Tversky ◽

Itamar Gati

Keyword(s):

Triangle Inequality

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Approximation in statistical sense to B -continuous functions by positive linear operators

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.2009.1129 ◽

2010 ◽

Vol 47 (3) ◽

pp. 289-298 ◽

Cited By ~ 2

Author(s):

Fadime Dirik ◽

Oktay Duman ◽

Kamil Demirci

Keyword(s):

Compact Subset ◽

Real Line ◽

Statistical Convergence ◽

Approximation Theorem ◽

Continuous Functions ◽

Linear Operators ◽

Positive Linear Operators ◽

Statistical Approximation ◽

Classical Version ◽

Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

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Roulette Wheel Selection based Heuristic Algorithm for the Orienteering Problem

INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY ◽

10.24297/ijct.v13i1.2933 ◽

2014 ◽

Vol 13 (1) ◽

pp. 4127-4145

Author(s):

Madhushi Verma ◽

Mukul Gupta ◽

Bijeeta Pal ◽

Prof. K. K. Shukla

Keyword(s):

Triangle Inequality ◽

Time Budget ◽

Control Point ◽

Hamiltonian Path ◽

Real Life ◽

Tourism Industry ◽

Orienteering Problem ◽

Complete Graphs ◽

Roulette Wheel Selection ◽

Roulette Wheel

Orienteering problem (OP) is an NP-Hard graph problem. The nodes of the graph are associated with scores or rewards and the edges with time delays. The goal is to obtain a Hamiltonian path connecting the two necessary check points, i.e. the source and the target along with a set of control points such that the total collected score is maximized within a specified time limit. OP finds application in several fields like logistics, transportation networks, tourism industry, etc. Most of the existing algorithms for OP can only be applied on complete graphs that satisfy the triangle inequality. Real-life scenario does not guarantee that there exists a direct link between all control point pairs or the triangle inequality is satisfied. To provide a more practical solution, we propose a stochastic greedy algorithm (RWS_OP) that uses the roulette wheel selectionmethod, does not require that the triangle inequality condition is satisfied and is capable of handling both complete as well as incomplete graphs. Based on several experiments on standard benchmark data we show that RWS_OP is faster, more efficient in terms of time budget utilization and achieves a better performance in terms of the total collected score ascompared to a recently reported algorithm for incomplete graphs.

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Almost Somewhat Near Continuity and Near Regularity

Moroccan Journal of Pure and Applied Analysis ◽

10.2478/mjpaa-2021-0009 ◽

2021 ◽

Vol 7 (1) ◽

pp. 88-99

Author(s):

Zanyar A. Ameen

Keyword(s):

Continuous Function ◽

Continuous Functions ◽

One To One ◽

Nearly Continuous

AbstractThe notions of almost somewhat near continuity of functions and near regularity of spaces are introduced. Some properties of almost somewhat nearly continuous functions and their connections are studied. At the end, it is shown that a one-to-one almost somewhat nearly continuous function f from a space X onto a space Y is somewhat nearly continuous if and only if the range of f is nearly regular.

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Approximating Continuous Functions by Iterated Function Systems and Optimization

SSRN Electronic Journal ◽

10.2139/ssrn.616605 ◽

2002 ◽

Author(s):

Davide La Torre ◽

Matteo Rocca

Keyword(s):

Iterated Function Systems ◽

Continuous Functions ◽

Iterated Function

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On existence result of a class of nonlinear integral equation

Filomat ◽

10.2298/fil1711593b ◽

2017 ◽

Vol 31 (11) ◽

pp. 3593-3597

Author(s):

Ravindra Bisht

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Existence And Uniqueness ◽

Existence Result ◽

Nonlinear Integral Equation ◽

Continuous Functions ◽

Concave Functions ◽

Real Numbers ◽

Fixed Point Techniques ◽

Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

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