Generalization of α-G-Contractions to j-G-Contractions on Uniform Spaces
Keywords:
Uniform spaces, Fixed point theory, j-G-contractions, Picard operatorAbstract
This work introduces the concept of j-G-contractions on uniform spaces generated by a saturated collection of pseudo metrics, extending the theoretical framework of α-G-contractions. Two main theorems are presented, both of which establish that if the map satisfies certain conditions, then it is a Picard operator. The first theorem relies on conditions defined by the structure of the space and graph, while the second theorem utilizes conditions related to orbital G-continuity. Criteria are provided for verifying j-G-contraction conditions, and it is shown that these maps satisfy the conditions of the main theorems. Some findings demonstrate that modifying the graph to satisfy j-G-contraction conditions can lead to an enlarged convergence set.
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