$$\alpha $$-Firmly nonexpansive operators on metric spaces

We extend to p-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise averaged mappings. Our main contribution is establishing a calculus for these mappings in p-uniformly convex spaces, showing in particular how the property is preserved under compositions and convex combinations. This is of central importance to splitting algorithms that are built by such convex combinations and compositions, and reduces the convergence analysis to simply verifying that the individual components have the required regularity pointwise at fixed points of the splitting algorithms. Our convergence analysis differs from what can be found in the previous literature in that the regularity assumptions are only with respect to fixed points. Indeed we show that, if the fixed point mapping is pointwise nonexpansive at all cluster points, then these cluster points are in fact fixed points, and convergence of the sequence follows. Additionally, we provide a quantitative convergence analysis built on the notion of gauge metric subregularity, which we show is necessary for quantifiable convergence estimates. This allows one for the first time to prove convergence of a tremendous variety of splitting algorithms in spaces with curvature bounded from above.

New Results on I 2 -Statistically Limit Points and I 2 -Statistically Cluster Points of Sequences of Fuzzy Numbers

In this paper, some existing theories on convergence of fuzzy number sequences are extended to I 2 -statistical convergence of fuzzy number sequence. Also, we broaden the notions of I -statistical limit points and I -statistical cluster points of a sequence of fuzzy numbers to I 2 -statistical limit points and I 2 -statistical cluster points of a double sequence of fuzzy numbers. Also, the researchers focus on important fundamental features of the set of all I 2 -statistical cluster points and the set of all I 2 -statistical limit points of a double sequence of fuzzy numbers and examine the relationship between them.

Limits, Sequences, and Sums

This chapter first introduces the concepts of real sequences, Cauchy sequences, limits, and cluster points. The chapter then discusses functions of a real variable, continuity concepts, convergence concepts for sequences of functions, summability and order of magnitude relations, inequalities for sums, regular variation, and limit concepts for arrays.

Further aspects of I K-convergence in topological spaces

In this paper, we obtain some results on the relationships between different ideal convergence modes namely, I K, I K∗ , I, K, I ∪ K and (I ∪K) ∗ . We introduce a topological space namely I K-sequential space and show that the class of I K-sequential spaces contain the sequential spaces. Further I K-notions of cluster points and limit points of a function are also introduced here. For a given sequence in a topological space X, we characterize the set of I K-cluster points of the sequence as closed subsets of X.

K-affinity propagation clustering algorithm for the classification of part-time workers using the internet

There has been a significant increase in the number of part-time workers in the last 3 years. Data collected from sakernas BPS showed that the number of part-time workers was 125,443,748 in the second period of 2016. This number rapidly increased in 2017, 2018 and 2019 in the same period, by 128,062,746, 131,005,641, and 133,560,880 workers. Based on the increase in the last 3 years, East Java province has the highest number of part-time workers that use the internet. This research aims to determine the number of part-time workers that use the internet by using the k-affinity propagation (K-AP) clustering. This method is used to produce the optimal number of cluster points (exemplar) is the affinity propagation (AP). Three clusters were used to determine the sum of the smallest value ratio. The result showed that clusters 1, 2, and 3 have 3, 23, and 5 members in Bondowoso, Jombang, and Surabaya districts.

SOME PROPERTIES OF EQUIDISTRIBUTED AND WELL DISTRIBUTED SEQUENCES

Many authors studied properties related to distribution and summability of sequences of real numbers. In these studies, different types of limit points of a sequence were introduced and studied including statistical and uniform statistical cluster points of a sequence. In this paper, we aim to prove some new results about the nature of different types of limit points, this time connected to equidistributed and well distributed sequences.

On rough convergence in amenable semigroups and some properties

The authors of the present paper, firstly, investigated relations between the notions of rough convergence and classical convergence, and studied on some properties of the rough convergence notion which the set of rough limit points and rough cluster points of a sequence of functions defined on amenable semigroups. Then, they examined the dependence of r-limit LIMrf of a fixed function f ∈ G on varying parameter r.

On I-statistically ϕ-convergence

In this paper we investigate the notion of I-statistical ϕ-convergence and introduce IS-ϕ limit points and IS-ϕ cluster points of real number sequence and also studied some of its basic properties.

On I-statistically limit points and I-statistically cluster points of sequences of fuzzy numbers

The main aim of this paper is to introduce I-st limit points and I-st cluster points of a sequence of fuzzy numbers and also study some of its basic properties. Conditions for a I-st limit point of a I-st cluster point are investigated.