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In this paper, we introduce new nonlinear iterative algorithms. These algorithms are used to study the convergence of generated iterative sequences in modular spaces. Moreover, we introduce a new double sequence iteration and prove that sequences converge strongly to a fixed point of a ρ-quasi contraction mapping in modular spaces. Finally, some illustrative numerical examples (using the Matlab software) are presented.

Nonlinear iterative algorithms for quasi contraction mapping in modular space