In this article, some common fixed point theorems for two pairs of compatible mappings together with sub-sequential continuity (alternately sub-compatible mappings together with reciprocal continuity) are proved in the setting of cone metric spaces. Our results are new in this setting especially in view of the note given in Imdad et al. [15]. On the other hand some fixed point results for faintly compatible mappings are also established. Illustrative examples along with their pictorial representation are furnished to highlight the validity of the hypothesis of our results

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In this note, we establish the existence of fixed point through fixed point theorems in the setting of partially ordered complex valued b-metric spaces. Then this fixed point is co-related as solution of equivalent operator equation of the Urysohn integral equation. In this process to make our results more authentic and meaningful we adopt an innovative way through visualling the given example supporting our findings. Naturally our results generalize some existing results.