In this paper, we have obtained two theorems for N\"orlund summability of Fourier series and their conjugate series under very general conditions. These two theorems are closely related to the great works of the analysts Patti \cite{20}, McFadden \cite{22} and Siddiqui \cite{23} but not the same. Manuscript profile

‎In this paper‎, ‎we prove some results on complex partial b-metric space $(\Re‎, ‎p_{b}^{c})$‎, ‎which are more generalization of S-contractive mappings‎. ‎Also‎, ‎we expand weakly increasing mappings of S-contractive for two self-mappings and prove some common fixed point theorems with supported examples in complete partial b-metric spaces $(\Re‎, ‎p_{b}^{c})$‎. Manuscript profile