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This paper introduces new types of the generalized C-condition for mappings in partially ordered modular metric spaces. For such conditions, the fixed point theorems are stated and proved. Some examples with graphical representation are given to support our findings. An integral equation is considered in the given modular metric space. The existence and also uniqueness of a solution for this equation are proved. These outcomes extend the fixed point results for the generalized C-condition to partially ordered modular metric spaces.
Gündoğdu et al. (2024) studied this question.