A New General System of Generalized Nonlinear Mixed Composite‐Type Equilibria and Fixed Point Problems with an Application to Minimization Problems

Pongsakorn Sunthrayuth and Poom Kumam

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: We introduce a new general system of generalized nonlinear mixed composite‐type equilibria and propose a new iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a general system of generalized nonlinear mixed composite‐type equilibria, and the set of fixed points of a countable family of strict pseudocontraction mappings. Furthermore, we prove the strong convergence theorem of the purposed iterative scheme in a real Hilbert space. As applications, we apply our results to solve a certain minimization problem related to a strongly positive bounded linear operator. Finally, we also give a numerical example which supports our results. The results obtained in this paper extend the recent ones announced by many others.

Date: 2012
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https://doi.org/10.1155/2012/414718

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:414718

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