the main purpose of this paper is to consider the t-best simultaneousapproximation in fuzzy normed spaces. we develop the theory of t-bestsimultaneous approximation in quotient spaces. then, we discuss the relationshipin t-proximinality and t-chebyshevity of a given space and its quotientspace.

Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the  set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.

This article is concerned with the approximation of unbounded convex sets by polyhedra. While there an abundance literature investigating this task for compact sets, results on case are scarce. We first point out connections between existing before introducing a new notion polyhedral called ($\varepsilon,\delta$)-approximation that integrates in meaningful way. Some basic about ($\varepsilon,\d...

In this paper, we consider the problem of maximizing a monotone submodular function subject to knapsack constraint in streaming setting. such setting, elements arrive sequentially and at any point time, algorithm can store only small fraction that have arrived so far. For special case all unit sizes (i.e., cardinality-constraint case), one find $$(0.5-\varepsilon )$$ -approximate solution $$O(K...

We study the early work scheduling problem on identical parallel machines in order to maximize total work, i.e., parts of non-preemptive jobs that are executed before a common due date. By preprocessing and constructing an auxiliary instance which has several good properties, for any desired accuracy $$\varepsilon $$ , we propose efficient polynomial time approximation scheme with running $$O\l...

Given a set P of points and U axis-parallel unit squares in the Euclidean plane, minimum ply cover with is subset that covers minimizes number share common intersection, called U. Biedl et al. [Comput. Geom., 94:101712, 2020] showed determining for by NP-hard, gave polynomial-time 2-approximation algorithm instances which constant. The question whether there exists approximation remained open w...

This paper is an attempt to prove the following result:Let $n>1$ be an integer and let $mathcal{R}$ be a $n!$-torsion-free ring with the identity element. Suppose that $d, delta, varepsilon$ are additive mappings satisfyingbegin{equation}d(x^n) = sum^{n}_{j=1}x^{n-j}d(x)x^{j-1}+sum^{n-1}_{j=1}sum^{j}_{i=1}x^{n-1-j}Big(delta(x)x^{j-i}varepsilon(x)+varepsilon(x)x^{j-i}delta(x)Big)x^{i-1}quadend{e...

The problem of finding \emph{distance} between \emph{pattern} of length $m$ and \emph{text} of length $n$ is a typical way of generalizing pattern matching to incorporate dissimilarity score. For both Hamming and $L_1$ distances only a super linear upper bound $\widetilde{O}(n\sqrt{m})$ are known, which prompts the question of relaxing the problem: either by asking for $1 \pm \varepsilon$ appro...

An upper dominating set is a minimal in graph. In the Upper Dominating Set problem, goal to find an of maximum size. We study complexity parameterized algorithms for Set, as well its sub-exponential approximation. First, we prove that, under ETH, k -Upper cannot be solved time \(O(n^{o(k)})\) (improving on \(O(n^{o(\sqrt{k})})\)), and same show assumption that any constant ratio r \(\varepsilon...