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Implicit contractive mappings in modular metric and fuzzy metric spaces
1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
Thescientificworldjournal
|July 9, 2014
Summary
This study explores fixed points in modular metric spaces, a generalization of classical modulars. New theorems are established for various contraction types and fuzzy metric spaces, with examples demonstrating applicability.
Area of Science:
- Mathematical Analysis
- Topology
- Functional Analysis
Background:
- Modular metric spaces generalize classical modulars like Lebesgue and Orlicz spaces.
- Recent introduction of modular metric spaces necessitates further investigation into their properties.
Purpose of the Study:
- To investigate the existence of fixed points for generalized α-admissible modular contractive mappings.
- To extend fixed point theory to partially ordered modular metric spaces and Suzuki-type contractions.
- To explore connections between fuzzy metric and modular metric spaces for new fixed point results.
Main Methods:
- Utilizing principles of fixed point theory in the context of modular metric spaces.
- Developing generalized α-admissible modular contractive mappings.
- Applying fixed point theorems to derive results for integral contractions and partially ordered spaces.
- Establishing a relationship between fuzzy and modular metrics to analyze triangular fuzzy metric spaces.
Main Results:
- Existence theorems for fixed points of generalized α-admissible modular contractive mappings.
- New fixed point theorems in partially ordered modular metric spaces.
- Suzuki-type fixed point theorems in modular metric spaces.
- Novel fixed point theorems for integral contractions.
- New fixed point results in triangular fuzzy metric spaces derived from the fuzzy-modular metric relation.
Conclusions:
- The study successfully establishes new fixed point theorems in modular metric spaces and their extensions.
- The findings contribute to the understanding of fixed point theory in generalized metric spaces.
- The established relation between fuzzy and modular metrics opens avenues for further research in fuzzy analysis.
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