1. NEW CONVERGENCE DEFINITIONS FOR DOUBLE SEQUENCES IN g-METRIC SPACES.
- Author
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GURDAL, MEHMET, KIşI, öMER, and KOLANCI, SAIME
- Subjects
METRIC spaces ,STOCHASTIC convergence ,CAUCHY sequences ,SUMMABILITY theory ,MATHEMATICAL sequences - Abstract
In this paper, we define g-convergence and g-Cauchy of double sequences in g-metric spaces. Also we prove that g-limit is unique and every g-convergent double sequence is a g-Cauchy sequence. Additionally g-statistical convergence of double sequences is introduced and the theorem giving the relationship between statistical convergence and strongly Cesáro summability in a g-metric space is demonstrated. Further, we put forward the notations of g-lacunary statistical convergence and g-strongly lacunary convergence of double sequences and we also present some inclusion theorems. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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