In this paper, we introduce a class of coupled large contractions for mixed monotone mappings in partially ordered metric spaces. The proposed contractive condition extends the classical coupled contraction of Bhaskar and Lakshmikantham by replacing the fixed Lipschitz constant with a Burton-type nonuniform contractive condition. Under suitable monotonicity and order assumptions, we establish the existence of coupled fixed points for mappings $ F:X\times X\rightarrow X $. An example is presented to show that the obtained result is not covered by the classical theorem of Bhaskar and Lakshmikantham. Additionally, we derive a uniqueness criterion and obtain a fixed point result for the associated single-valued mapping $ f:X\rightarrow X $ defined by $ f(x) = F(x, x) $.
Citation: Mouataz Billah Mesmouli, Doha A. Abulhamil, Ovidiu Popescu. Coupled fixed point results for Burton-type large contractions in partially ordered metric spaces[J]. AIMS Mathematics, 2026, 11(8): 26226-26245. doi: 10.3934/math.20261051
In this paper, we introduce a class of coupled large contractions for mixed monotone mappings in partially ordered metric spaces. The proposed contractive condition extends the classical coupled contraction of Bhaskar and Lakshmikantham by replacing the fixed Lipschitz constant with a Burton-type nonuniform contractive condition. Under suitable monotonicity and order assumptions, we establish the existence of coupled fixed points for mappings $ F:X\times X\rightarrow X $. An example is presented to show that the obtained result is not covered by the classical theorem of Bhaskar and Lakshmikantham. Additionally, we derive a uniqueness criterion and obtain a fixed point result for the associated single-valued mapping $ f:X\rightarrow X $ defined by $ f(x) = F(x, x) $.
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Mouataz Billah Mesmouli, Doha A. Abulhamil, Ovidiu Popescu. Coupled fixed point results for Burton-type large contractions in partially ordered metric spaces[J]. AIMS Mathematics, 2026, 11(8): 26226-26245. doi: 10.3934/math.20261051
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