In this paper, we introduced the strong-controlled Branciari $ b $-distance, a generalized metric structure designed to consolidate disparate fixed point theorems scattered throughout existing literature. Through illustrative examples, we demonstrated how this framework subsumes and extends previous results. We further established the applicability of our theoretical developments by presenting a concrete problem whose solution leverages the properties of strong-controlled Branciari $ b $-distance spaces.
Citation: Dania Santina, Wan Ainun Mior Othman, Kok Bin Wong, Nabil Mlaiki. New developments in fixed point theorems for $ \theta $-Branciari contractions on strong-controlled Branciari $ b $ distance spaces[J]. AIMS Mathematics, 2025, 10(12): 28100-28114. doi: 10.3934/math.20251235
In this paper, we introduced the strong-controlled Branciari $ b $-distance, a generalized metric structure designed to consolidate disparate fixed point theorems scattered throughout existing literature. Through illustrative examples, we demonstrated how this framework subsumes and extends previous results. We further established the applicability of our theoretical developments by presenting a concrete problem whose solution leverages the properties of strong-controlled Branciari $ b $-distance spaces.
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Dania Santina, Wan Ainun Mior Othman, Kok Bin Wong, Nabil Mlaiki. New developments in fixed point theorems for $ \theta $-Branciari contractions on strong-controlled Branciari $ b $ distance spaces[J]. AIMS Mathematics, 2025, 10(12): 28100-28114. doi: 10.3934/math.20251235
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