We introduce and study the general nonlinear random H, η -accretive equations with random fuzzy mappings. By using the resolvent technique for the H, η -accretive operators, we prove the existence theorems and convergence theorems of the generalized random iterative algorithm for this nonlinear random equations with random fuzzy mappings in q-uniformly smooth Banach spaces. Our result in this paper improves and generalizes some known corresponding results in the literature.

In this paper, we introduce and study iterative algorithms for solving split mixed equilibrium problems and fixed point problems of λ-hybrid multivalued mappings in real Hilbert spaces and prove that the proposed iterative algorithm converges weakly to a common solution of the considered problems. We also provide an example to illustrate the convergence behavior of the proposed iteration process.

In this article, we introduce a new iterative scheme for finding a common element of the set of fixed points of strongly relatively nonexpansive mapping, the set of solutions for equilibrium problems and the set of zero points of maximal monotone operators in a uniformly smooth and uniformly convex Banach space. Consequently, we obtain new strong convergence theorems in the frame work of Banach spaces. Our theorems extend and improve the recent results of Wei et al., Takahashi and Zembayashi, and some recent results.

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