Solvability of Systems of Integral Equations by using the Mixed Monotone Property in Partially Ordered Metric Spaces

Reza Allahyari; Ali Shole Haghighi; Hassan Khosravi

doi:https://doi.org/10.14445/22315373/IJMTT-V12P508

International Journal of Mathematics Trends and Technology

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Volume 12 | Number 1 | Year 2014 | Article Id. IJMTT-V12P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V12P508

Solvability of Systems of Integral Equations by using the Mixed Monotone Property in Partially Ordered Metric Spaces

Reza Allahyari, Ali Shole Haghighi, Hassan Khosravi

Abstract

The purpose of this work is to present some existence results of solutions for a class of systems of mixed monotone mappings in partially ordered metric spaces. The results of this work are extensions and generalizations of known coupled and tripled fixed point results. The methods of proofs used in this paper, show that most of new coupled and tripled fixed point results are merely reformulation of some fixed point results in the literature. As an interesting application of our results, we discuss the existence and uniqueness of solutions for a class of systems of nonlinear integral equations.xi(t)=fi (t,x1(t),…,xn(t),∫a(β_i (t))gi(t,s,x1(s),…,xn (s))ds). Finally, an example is presented to show the efficiency of our results.

Keywords

System of Integral Equations, Mixed Monotone Property, Partially Ordered Set, Fixed Point.

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Citation :

Reza Allahyari, Ali Shole Haghighi, Hassan Khosravi, "Solvability of Systems of Integral Equations by using the Mixed Monotone Property in Partially Ordered Metric Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 12, no. 1, pp. 47-57, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V12P508