TAILIEUCHUNG - Some results on uniform statistical cluster points

In this paper, we present some results linking the uniform statistical limit superior and inferior, almost convergence and uniform statistical convergence of a sequence. We also study the relationship between the set of uniform statistical cluster points of a given sequence and its subsequences. | Turk J Math (2017) 41: 1133 – 1139 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article Some results on uniform statistical cluster points ˙ 1,∗, Leila MILLER-VAN-WIEREN2 Tu˘ gba YURDAKADIM 1 Department of Mathematics, Hitit University, C ¸ orum, Turkey 2 Faculty of Engineering and Natural Sciences, International University of Sarajevo, Sarajevo, Bosnia and Herzegovina Received: • Accepted/Published Online: • Final Version: Abstract: In this paper, we present some results linking the uniform statistical limit superior and inferior, almost convergence and uniform statistical convergence of a sequence. We also study the relationship between the set of uniform statistical cluster points of a given sequence and its subsequences. The results concerning uniform statistical convergence and uniform statistical cluster points presented here are also closely related to earlier results regarding statistical convergence and statistical cluster points of a sequence. Key words: Uniform statistical convergence, subsequences, uniform statistical cluster points 1. Introduction The convergence of sequences has undergone numerous generalizations in order to provide deeper insights into summability theory. Convergence of sequences has different generalizations. One of the most important generalizations is uniform statistical convergence. This type of convergence has been introduced by Brown and Freedman [3] by using uniform density and has been studied by many authors in various directions [2, 14, 15, 19, 20]. This type of convergence is stronger than ordinary convergence and so it is quite effective, especially when the classical limit does not exist. Buck [5] initiated the study of the relationship between the convergence of a given sequence and the summability of its subsequences. Later Agnew [1], Buck [6], Buck and Pollard [7], Miller and Orhan [18], and Zeager [22] .

• Toán học
• Uniform statistical convergence
• Uniform statistical cluster points
• Uniform statistical limit superior
• Asymptotic density
• Summability of subsequences