The first observational evidence for the cosmic acceleration appeared from the type Ia supernovae (SNe Ia) Hubble diagram from two different groups. However, the empirical treatment of SNe Ia and their ability to show cosmic acceleration have been the subject of some debate in the literature. In this work we probe the assumption of redshift-independent absolute magnitude $(M_{mathrm{B}})$ of SNe along with its correlation with spatial curvature ($Omega_{k0}$) and cosmic distance duality relation (CDDR) parameter ($eta(z)$). This work is divided into two parts. Firstly, we check the validity of CDDR which relates the luminosity distance ($d_L$) and angular diameter distance ($d_A$) via redshift. We use three different redshift-dependent parametrizations of the distance duality parameter $(eta(z))$. CDDR is fairly consistent for almost every parametrization within $95%$ confidence level in both flat and non-flat universe. However, one of the parametrizations does not validate CDDR in the case of a non-flat universe. In second part, we take the validity of CDDR for granted and emphasise on the variability of $M_{mathrm{B}}$ and its correlation with $Omega_{k0}$. We choose three different redshift-dependent parametrizations of $M_{mathrm{B}}$. The results indicate no evolution of $M_{mathrm{B}}$ at $99%$ confidence level but clearly indicates the inclination towards a non-flat open universe. We further extend our analysis and examine the dependence of the results on the choice of different priors for $H_0$.
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