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In the present paper, we examine the perturbation of continuous frames and Riesz-type frames in Hilbert C * -modules. We extend the Casazza–Christensen general perturbation theorem for Hilbert space frames to continuous frames in Hilbert C * -modules. We obtain a necessary condition under which the perturbation of a Riesz-type frame of Hilbert C * -modules remains to be a Riesz-type frame. Also, we examine the effect of duality on the perturbation of continuous frames in Hilbert C * -modules, and we prove that if the operator frame of a continuous frame F is near to the combination of the synthesis operator of a continuous Bessel mapping G and the analysis operator of F, then G is a continuous frame. [ABSTRACT FROM AUTHOR]

In the present paper a concept of $$C^*$$ -algebra-valued modular space is introduced which is a generalization of a modular space. Next, some fixed point theorems for self-maps with contractive or expansive conditions on such spaces are proved. [ABSTRACT FROM AUTHOR]