The purpose of this paper is to propose an iterative algorithm for equilibrium problem and a class of strictly pseudononspreading mappings which is more general than the class of nonspreading mappings studied recently in Kurokawa and Takahashi (2010). We explored an auxiliary mapping in our theorems and proofs and under suitable conditions, some weak and strong convergence theorems are proved. The results presented in the paper extend and improve some recent results announced by some authors.

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In this paper, properties for Hamiltonian semirings are studied. We concluded that subsemirings and all homomorphic images of a Hamiltonian semiring are Hamiltonian semirings. Hamiltonian semirings satisfying the congruence extension property are characterized by the strong congruence extension property. Finally, we concluded that if R × R is a Hamiltonian semiring, then R has strong congruence extension property

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