scholarly journals Some Remarks on The Paper "Global Optimization in Metric Spaces With Partial Orders"

2021 ◽  
Vol 2 (1) ◽  
pp. 71-78
Author(s):  
Moosa Gabeleh ◽  
Jack Markin ◽  
◽  
Keyword(s):  
Global Optimization ◽  
Metric Spaces ◽  
Partial Orders

Global optimization in metric spaces with partial orders

Optimization ◽  
2012 ◽  
Vol 63 (5) ◽  
pp. 817-825 ◽  
Author(s):  
S. Sadiq Basha
Keyword(s):  
Global Optimization ◽  
Metric Spaces ◽  
Partial Orders

scholarly journals Global optimization using $\alpha$-ordered proximal contractions in metric spaces with partial orders

2016 ◽  
Vol 17 (2) ◽  
pp. 173 ◽  
Author(s):  
Somayya Komal ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Global Optimization ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Orders ◽  
Proximal Contraction ◽  
Complete Metric Spaces ◽  
New Type ◽  
Frame Work

The purpose of this article is to establish the global optimization with partial orders for the pair of non-self mappings, by introducing new type of contractions like $\alpha$-ordered contractions and $\alpha$-ordered proximal contraction in the frame work of complete metric spaces. Also calculates some fixed point theorems with the help of these generalized contractions. In addition, established an example to show the validity of our main result. These results extended and unify many existing results in the literature.<br /><br />

scholarly journals On the foundations of final coalgebra semantics: non-well-founded sets, partial orders, metric spaces

1998 ◽  
Vol 8 (5) ◽  
pp. 481-540 ◽  
Author(s):  
DANIELE TURI ◽  
JAN RUTTEN
Keyword(s):  
Computer Science ◽  
Mathematical Theory ◽  
Metric Spaces ◽  
Operational Semantics ◽  
Denotational Semantics ◽  
Partial Orders ◽  
Present Survey ◽  
Induction Principle ◽  
Structural Operational Semantics ◽  
Modern Mathematics

This paper, a revised version of Rutten and Turi (1993), is part of a programme aiming at formulating a mathematical theory of structural operational semantics to complement the established theory of domains and denotational semantics to form a coherent whole (Turi 1996; Turi and Plotkin 1997). The programme is based on a suitable interplay between the induction principle, which pervades modern mathematics, and a dual, non-standard ‘coinduction principle’, which underlies many of the recursive phenomena occurring in computer science.The aim of the present survey is to show that the elementary categorical notion of a final coalgebra is a suitable foundation for such a coinduction principle. The properties of coalgebraic coinduction are studied both at an abstract categorical level and in some specific categories used in semantics, namely categories of non-well-founded sets, partial orders and metric spaces.

scholarly journals The partially ordered family of all ℛ-classes of S(x)

1983 ◽  
Vol 26 (1) ◽  
pp. 7-13 ◽  
Author(s):  
K. D. Magill
Keyword(s):  
Topological Space ◽  
Metric Spaces ◽  
Partial Orders ◽  
Partially Ordered

Let S(X) denote the semigroup of all continuous selfmaps of the topological space X. Let ℒ(S(X)) and ℛ(S(X)) denote the partially ordered families of all ℒ-classes and ℛ-classes, respectively, of S(X) where the partial orders are the usual ones [3, p. 29]. In [6] we made the followingConjecture. The following statements are equivalent about any two compact 0-dimensional metric spaces X and Y:(1) ℒ(S(X)) and ℒ(S(Y)) are order isomorphic.(2) ℛ(S(X)) and (S{Y)) are order isomorphic.(3) The semigroupsS(X) and S(Y) are isomorphic.(4) The spaces X and Y are homeomorphic.

scholarly journals Extendible spaces

2002 ◽  
Vol 3 (2) ◽  
pp. 169 ◽  
Author(s):  
M.P. Schellekens
Keyword(s):  
Partial Order ◽  
Metric Spaces ◽  
Extension Property ◽  
Partial Orders ◽  
Domain Theory ◽  
Extremal Element

<p>The domain theoretic notion of lifting allows one to extend a partial order in a trivial way by a minimum. In the context of Quantitative Domain Theory partial orders are represented as quasi-metric spaces. For such spaces, the notion of the extension by an extremal element turns out to be non trivial.</p><p>To some extent motivated  by these considerations, we characterize the directed quasi-metric spaces extendible by an extremum. The  class is shown to include the S-completable directef quasi-metric spaces. As an application of this result, we show that for the case of the invariant quasi-metric (semi)lattices, weightedness can be characterized by order convexity with the extension property.</p>

scholarly journals A Weak Tripled Contraction for Solving a Fuzzy Global Optimization Problem in Fuzzy Metric Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 565
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Global Optimization ◽  
Metric Space ◽  
Optimization Problem ◽  
Metric Spaces ◽  
Point Problem ◽  
Global Optimization Problem ◽  
Tripled Fixed Point ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric

In the setting of fuzzy metric spaces (FMSs), a global optimization problem (GOP) obtaining the distance between two subsets of an FMS is solved by a tripled fixed-point (FP) technique here. Also, fuzzy weak tripled contractions (WTCs) for that are given. This problem was known before in metric space (MS) as a proximity point problem (PPP). The result is correct for each continuous τ−norms related to the FMS. Furthermore, a non-trivial example to illustrate the main theorem is discussed.

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