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Statistical convergence is an active area, and it appears in a wide variety of topics. However, it has not been studied extensively in Riesz spaces. There are a few studies about the statistical convergence on Riesz spaces, but they only focus on the relationship between statistical and order convergences of sequences in Riesz spaces. In this paper, we introduce the notion of (V, lambda)-order summable by using the concept of lambda-statistical monotone and the lambda-statistical order convergent sequences in Riesz spaces. Moreover, we give some relations between (V, lambda)-order summable and lambda-statistical order convergence.

In this paper, the concept of deferred statistical convergence is generalized to general metric spaces, and some inclusion relations between deferred strong Ces\`{a}ro summability and deferred statistical convergence are given in general metric spaces.

We give definition of (lambda,nu)(-) statistical convergence on a product time scale. Furthermore, we generalize de la Vallee Poussin mean and define strongly (V,lambda,nu) and [V,lambda,nu](psi 2)(p)(-) summable functions, statistical limit superior and inferior on a product time scale. Then, a few inclusion relations are expressed between the sets of (V,lambda,nu)(-)summable, (p-)strongly [V,lambda,nu](psi 2)(p)(-)summable and (lambda,nu)(-)statistical convergent functions. Furthermore, some theorems are proved related to statistical limit superior and inferior on a product time scale.

We introduce and examine the concepts of asymptotic statistical equivalence of order  , and strong  asymptotic equivalence of order of sequences. Also, we give some relations connected to these concepts.

SARI, Ismail/0000-0001-7737-4180; Tezcan, Mehmet Engin/0000-0002-1753-4936; TUFAN, Abdurrahman/0000-0001-6244-9362 WOS: 000417143401346 …

WOS: 000383727500007 In this paper we introduce the concepts of uniform and pointwise Delta(m) - statistical convergence of order alpha of sequence of functions. We also give notions of uniform and pointwise Delta(m) - statistically Cauchy sequence of order alpha of sequence of functions and show that pointwise Delta(m) - statistically Cauchy sequence (uniform Delta(m) -statistical convergence) is equivalent to pointwise Delta(m) - statistical convergence (uniform Delta(m) - statistically Cauchy sequence) of order alpha. Moreover, some relations between pointwise Delta(m) - statistical convergence of order alpha and strongly pointwise Delta(m)(q) - Cesaro summable of order alpha of sequence of functions are given. Management Union of the Scientific Research Projects of Firat UniversityFirat University [FUBAP FF.12.03] The authors thank the Management Union of the Scientific Research Projects of Firat University for its financial support under Grant No. FUBAP FF.12.03.

In this paper, we define a metric on our new space and then show that this linear metric space is k-nearly uniform convex and has property beta where p=(p(k)) is a bounded sequence of positive real numbers. Finally, we give a result about property (H) by using k-nearly uniform convexity.

In this study, we introduce the concepts of pointwise lambda-statistical convergence of order a and pointwise [V, lambda]-summability of order alpha of sequences of real valued functions. Some relations between S-lambda(alpha)(f)-statistical convergence and strong w(lambda p)(alpha)(f)-summability are given.

WOS: 000463722100007, PubMed ID: 30489254, Objective: Familial Mediterranean fever (FMF) is the most common autoinflammatory disease. Most of the identified disease-causing mutations are located on exon 10. As the number of studies about the effect of the exonal location of the mutation and its phenotypic expression is limited, we aimed to investigate whether the exonic location of the Mediterranean fever (MEFV) mutation has an effect on the clinical manifestation in patients with FMF. Methods: Study population was derived from the main FMF registry that included 2246 patients from 15 different rheumatology clinics. We categorized the mutations according to their exon locations and retrieved the clinical and demographic information from the database. Results: Patients having the MEFV mutations on exon 2 or 10 (n: 1526) were divided into three subgroups according to the location of the MEFV mutations: Group 1 (exon 2 mutations), Group 2 (exon 10 mutations), and Group 3 (both exon 2 and exon 10 mutations). Group 2 patients were of a significantly younger age at onset, and erysipel-like erythema, arthritis, amyloidosis, and a family history of FMF were more common in this group. Conclusion: Patients with FMF and exon 10 mutations show more severe clinical symptoms and outcome. Exon 2 mutations tend to have a better outcome.