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Strongly lacunary ward continuity in 2-normed spaces
Hüseyin Çakalli1, Sibel Ersan2
1Department of Mathematics, Maltepe University, Marmara Eğitim Köyü, 34857 İstanbul, Turkey.
Thescientificworldjournal
|July 23, 2014
Summary
This study introduces strongly lacunary ward continuity for functions in 2-normed spaces. It explores how this continuity property preserves specific types of sequences, advancing the understanding of function behavior in these mathematical spaces.
Area of Science:
- Mathematics
- Functional Analysis
- Topology
Background:
- The study of continuity in normed spaces is a fundamental area of mathematical analysis.
- Investigating generalized forms of continuity, such as lacunary ward continuity, extends existing theories.
- 2-normed spaces offer a framework for generalizing concepts from standard normed spaces.
Purpose of the Study:
- To define and investigate strongly lacunary ward continuity for functions on subsets of 2-normed spaces.
- To analyze the preservation of strongly lacunary quasi-Cauchy sequences under this new continuity definition.
- To explore other related continuity concepts within the context of 2-normed spaces.
Main Methods:
- Definition of strongly lacunary ward continuity based on the preservation of strongly lacunary quasi-Cauchy sequences.
- Theoretical analysis of the properties of functions exhibiting this type of continuity in 2-normed spaces.
- Comparative study with other existing continuity notions in 2-normed spaces.
Main Results:
- Established the definition of strongly lacunary ward continuity.
- Demonstrated that functions exhibiting this continuity preserve strongly lacunary quasi-Cauchy sequences.
- Initiated the investigation into other related continuity types in 2-normed spaces.
Conclusions:
- Strongly lacunary ward continuity provides a new perspective on function behavior in 2-normed spaces.
- The preservation of specific sequence types is a key characteristic of this continuity.
- This work lays the groundwork for further research into generalized continuity in 2-normed spaces.
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