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In this paper, based on [A. Razani, V. Rakočcević and Z. Goodarzi, Nonself mappings in modular spaces and common fixed point theorems, Cent. Eur. J. Math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping T in the modular space Xρ is presented. Moreover, we study a new version of Krasnoseleskii's fixed point theorem for S + T, where T is a continuous nonself contraction mapping and S is continuous mapping such that S(C) resides in a compact subset of Xρ, where C is a nonempty and complete subset of Xρ, also C is not bounded. Our result extends and improves the result announced by Hajji and Hanebally [A. Hajji and E. Hanebaly, Fixed point theorem and its application to perturbed integral equations in modular function spaces, Electron. J. Differ. Equ. 2005 (2005) 1-11]. As an application, the existence of a solution of a nonlinear integral equation on C(I, Lφ) is presented, where C(I, Lφ) denotes the space of all continuous function from I to Lφ, Lφ is the Musielak-Orlicz space and I = [0, b] ⊂ R. In addition, the concept of quasi contraction non-self mapping in modular space is introduced. Then the existence of a fixed point of these kinds of mapping without ∆2-condition is proved. Finally, a three step iterative sequence for non-self mapping is introduced and the strong convergence of this iterative sequence is studied. Our theorem improves and generalized recent know results in the literature. [ABSTRACT FROM AUTHOR]