Abstract
Let E be a Banach space with a cone P. Let \(T,\varphi _i: E\rightarrow E\) (\(i=1,2\)) be three given operators. We address the following question: Find \(x\in E\) such that
where \(\le _P\) is the partial order on E induced by the cone P , and \(0_E\) is the zero vector of E. We obtain sufficient conditions for the existence and uniqueness of solutions to this problem. We present an iterative algorithm to approximate the solution. The error estimates as well as results concerning the data dependence , well-posedness , limit shadowing property, and sequences of operators are provided. Some interesting consequences are deduced from our main results.
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Jleli, M., Karapinar, E., Samet, B. (2017). On the Approximation of Solutions to a Fixed Point Problem with Inequality Constraints in a Banach Space Partially Ordered by a Cone. In: Banaś, J., Jleli, M., Mursaleen, M., Samet, B., Vetro, C. (eds) Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness. Springer, Singapore. https://doi.org/10.1007/978-981-10-3722-1_12
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DOI: https://doi.org/10.1007/978-981-10-3722-1_12
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