# SOME FIXED POINT THEOREMS IN GENERALIZED DARBO FIXED POINT THEOREM AND THE EXISTENCE OF SOLUTIONS FOR SYSTEM OF INTEGRAL EQUATIONS

• Arab, Reza (Department of Mathematics, Sari Branch Islamic Azad University)
• Published : 2015.01.01
• 79 8

#### Abstract

In this paper we introduce the notion of the generalized Darbo fixed point theorem and prove some fixed and coupled fixed point theorems in Banach space via the measure of non-compactness, which generalize the result of Aghajani et al. [6]. Our results generalize, extend, and unify several well-known comparable results in the literature. One of the applications of our main result is to prove the existence of solutions for the system of integral equations.

#### Keywords

measure of noncompactness;fixed point;coupled fixed point;system of integral equations

#### References

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2. Existence of solutions for a class of system of functional integral equation via measure of noncompactness vol.313, 2017, https://doi.org/10.1016/j.cam.2016.09.011
3. The behaviour of measures of noncompactness in $$L^\infty ({\mathbb {R}}^n)$$ L ∞ ( R n ) with application to the solvability of functional integral equations 2017, https://doi.org/10.1007/s13398-017-0397-4
4. Darbo type fixed and coupled fixed point results and its application to integral equation vol.77, pp.1, 2018, https://doi.org/10.1007/s10998-017-0223-y
5. Existence of solutions to nonlinear functional-integral equations via the measure of noncompactness vol.20, pp.2, 2018, https://doi.org/10.1007/s11784-018-0546-1