Rough Convergence in Metric Spaces

Rough convergence of sequences in a partial metric space

“…Later though many authors carried out the works of rough convergence [2,9,10] in more generalized form. But the study of rough convergence in a metric space studied by S. Debnath and D. Rakhshit [7] and in a cone metric space studied by A. K. Banerjee and R. Mondal [4] are significant for our present works.…”

ON THE ROUGH CONVERGENCE OF A SEQUENCE OF SETS Vol. 10(1) Jan 2022, No. 14, pp. 167-174 OZNUR OLMEZ, FATMA GECIT AKC¸ AY AND SALIH AYTAR

“…Now we will define a new type of Hausdorff convergence for a sequence of closed sets. The concept of rough convergence in a metric space was first introduced by Debnath and Rakshit [3]. Since the set of all closed sets is a metric space with the Hausdorff metric, following definition is a special case of Debnath and Rakshit's [3] definition.…”

On Rough I–αβ–Statistical Convergence of Order γ in Intuitionistic Fuzzy Normed Spaces

“…To handle these types of problems, Phu [22] developed the idea of rough convergence in finite-dimensional normed linear spaces and later studied the same in an infinite-dimensional normed linear space [23]. This notion was further extended to rough statistical convergence [5] and rough I-convergence [10], and it was later analyzed in metric spaces [9] and intuitionistic fuzzy normed spaces [3]. In view of the recent applications of ideals and the αβ-density of order γ in the convergence theory, it is completely reasonable to explore the idea of rough I-αβ-convergence of order γ in the setting of intuitionistic fuzzy normed space.…”