On solving split equilibrium problems and fixed point problems of nonspreading multi-valued mappings in Hilbert spaces

Abstract

In this paper, we introduce and study iterative schemes for solving split equilibrium problems and fixed point problems of nonspreading multi-valued mappings in Hilbert spaces and prove that the modified Mann iteration converges weakly to a common solution of the considered problems. Moreover, we present some examples and numerical results for the main results. MSC: 47H10; 54H25

On solving split mixed equilibrium problems and fixed point problems of hybrid-type multivalued mappings in Hilbert spaces

“…Then we prove some weak convergence theorems which extend and improve the corresponding results of Kazmi and Rizvi [10] and Suantai et al [13] and many others. We finally provide numerical examples for supporting our main result.…”

A Hybrid Proximal Algorithm for the Sum of Monotone Operators with Multivalued Mappings

“…Lemma 2 (see [16]). Let be a nonempty closed convex subset of a Hilbert space and : → ( ) be a -nonspreading multivalued mapping with ∈ (0, 1/2].…”

“…Clearly, if is a 1/2-nonspreading and Fix( ) ̸ = 0, then is quasi-nonexpansive. Example in [16] shows that is a 1/2nonspreading multivalued mapping which is not nonexpansive.…”

“…For the extension of mappings, many authors have studied the convergence theorems of multivalued mappings (see [13][14][15]). In 2016, Suantai et al [16] considered iterative schemes for solving split equilibrium problems and fixed point problems of nonspreading multivalued mappings in Hilbert spaces and proved that the modified Mann iteration converges weakly to a common solution of the considered problems.…”

“…Inspired by [8,16], in this paper, we present the convergence analysis on the set Fix( ) ∩ ( + ) −1 (0), where is a nonspreading multivalued mapping in a Hilbert space. The results of this paper extend and improve some well-known results in the literature.…”