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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. [ABSTRACT FROM AUTHOR]

In this paper, we present some existence and uniqueness results for coupled coincidence point and common fixed point of θ- ψ-contraction mappings in complete metric spaces endowed with a directed graph. Our results generalize the results obtained by Kadelburg et al. (Fixed Point Theory Appl. 2015:27, , doi:). We also have an application to some integral system to support the results. [ABSTRACT FROM AUTHOR]

For the purpose of this paper, we use the method different from the relaxed extragradient method for finding a common element of the set of fixed points of a quasi-nonexpansive mapping, the set of solutions of equilibrium problems, and the set of solutions of a modified system of variational inequalities without demiclosed condition of W and $W_{\omega}:= (1-\omega )I+\omega W$, where W is a quasi-nonexpansive mapping and $\omega\in (0,\frac{1}{2} )$ in the framework of Hilbert space. By using our main result, we obtain a strong convergence theorem involving a finite family of nonspreading mappings and another corollary. Moreover, we give a numerical example to encourage our main theorem. [ABSTRACT FROM AUTHOR]

In this paper, we prove Browder's convergence theorem for G-nonexpansive mappings in a Hilbert space with a directed graph. Moreover, we also prove strong convergence of the Halpern iteration process to a fixed point of G-nonexpansive mappings in a Hilbert space endowed with a directed graph. The main results obtained in this paper extend and generalize many well-known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we construct an iterative process involving a hybrid pair of a finite family of generalized asymptotically nonexpansive single-valued mappings and a finite family of generalized nonexpansive multi-valued mappings and prove weak and strong convergence theorems of the proposed iterative process in Banach spaces. Our main results extend and generalize many results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a new type of G-contraction multivalued mappings in a metric space endowed with a directed graph is introduced and studied. This type of mappings is more general than that of Mizoguchi and Takahashi (J. Math. Anal. Appl. 141:177-188, 1989), Berinde and Berinde (J. Math. Anal. Appl. 326:772-782, 2007), Du (Topol. Appl. 159:49-56, 2012), and Sultana and Vetrivel (J. Math. Anal. Appl. 417:336-344, 2014). A fixed point and coincidence point theorem for this type of mappings is established. Some examples illustrating our main results are also given. The main results obtained in this paper extend and generalize those in (Tiammee and Suantai in Fixed Point Theory Appl. 2014:70, 2014) and many well-known results in the literature. [ABSTRACT FROM AUTHOR]

By using the concept of a class of functions, the $\mathcal {R}$-functions, we provide some fuzzy fixed point theorems on a space of fuzzy sets equipped with the supremum metric. By presenting a technique of constructing a sequence of successive approximations, we obtain some interesting results that improve many existing results. The related cases are also shown and discussed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of weak g-graph-preserving for multi-valued mappings and weak G-contractions in a metric space endowed with a directed graph. We establish the coincidence point theorems for this type of mappings in a complete metric space endowed with a directed graph. Examples illustrating our main results are also presented. Our results extend and generalize various known results in the literature. [ABSTRACT FROM AUTHOR]

In this article, we introduce composite iterative schemes for finding a zero point of a finite family of maximal monotone operators in a reflexive Banach space. Then, we prove strong convergence theorems by using a shrinking projection method. Moreover, we also apply our results to a system of convex minimization problems in reflexive Banach spaces. AMS Subject Classification: 47H09, 47H10 [ABSTRACT FROM AUTHOR]

We introduce a new iterative algorithm for a system of generalized equilibrium problems and a countable family of strict pseudocontractions in Hilbert spaces. We then prove that the sequence generated by the proposed algorithm converges strongly to a common element in the solutions set of a system of generalized equilibrium problems and the common fixed points set of an infinitely countable family of strict pseudocontractions. [ABSTRACT FROM AUTHOR]

We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemirelatively nonexpansive mapping in a Banach space by using monotone hybrid iteration method. By using these results, we obtain new convergence results for resolvents of maximal monotone operators and hemirelatively nonexpansive mappings in a Banach space. [ABSTRACT FROM AUTHOR]

We proposed in this paper a new iterative scheme for finding common elements of the set of fixed points of a finite family of quasi-nonexpansive mappings, the set of solutions of variational inclusion, and the set of solutions of generalized equilibrium problems. Some strong convergence results were derived by using the concept of W-mappings for a finite family of quasi-nonexpansive mappings. Strong convergence results are derived under suitable conditions in Hilbert spaces. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new algorithm for solving the split common fixed point problem for infinite families of demicontractive mappings. Strong convergence of the proposed method is established under suitable control conditions. We apply our main results to study the split common null point problem, the split variational inequality problem, and the split equilibrium problem in the framework of a real Hilbert space. A numerical example supporting our main result is also given. [ABSTRACT FROM AUTHOR]