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Fixed point theorems for generalized α -β-weakly contraction mappings in metric spaces and applications
Abdul Latif1, Chirasak Mongkolkeha2, Wutiphol Sintunavarat3
1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
Thescientificworldjournal
|June 5, 2014
Summary
Researchers introduce generalized alpha-beta-weakly contraction mappings, a new class that generalizes existing concepts. This work establishes fixed-point theorems in various metric spaces, expanding upon prior research in contraction mapping theory.
Area of Science:
- Mathematical Analysis
- Topology
- Fixed-Point Theory
Background:
- Introduces generalized alpha-beta-weakly contraction mappings, extending the concept of generalized weakly contraction mappings.
- Highlights the significance of this new class through illustrative examples, demonstrating its broader applicability compared to existing mappings.
Purpose of the Study:
- To establish novel fixed-point theorems for generalized alpha-beta-weakly contraction mappings in metric spaces.
- To demonstrate that the proposed class of mappings is a genuine generalization of several established classes.
Main Methods:
- Theoretical development of generalized alpha-beta-weakly contraction mappings.
- Establishment of fixed-point theorems using the properties of these new mappings.
- Application of the main results to various types of metric spaces, including those with binary relations and graphs.
Main Results:
- Demonstration that generalized alpha-beta-weakly contraction mappings represent a significant extension of existing contraction mapping concepts.
- Successful establishment of fixed-point results for these mappings in general metric spaces.
- Extension of fixed-point results to more complex settings: metric spaces with binary relations and metric spaces endowed with graphs.
Conclusions:
- The newly defined generalized alpha-beta-weakly contraction mappings offer a more comprehensive framework for fixed-point theory.
- The established fixed-point theorems provide valuable tools for solving equations in diverse mathematical spaces.
- This research contributes to the advancement of fixed-point theory by unifying and generalizing several existing results.
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