Addressing an open problem of Choudhury et al. “Fuzzy Sets Syst. 8 (2013), 84-97”

The question of relaxing the compatible hypothesis of the pair of mappings in fixed point theory has always been remained an open problem. We address such an open problem raised by Choudhury et al. [4] and also explicitly settles the issue of monotone and continuity hypotheses of the involved mappings in coupled coincidence point results. Moreover, we state a gap in an example given in [3] and repair it. Application to the dynamic programming problem shows the usability of present work. Finally, we also propose an open problem for further investigation.