We introduce a new iterative scheme for finding the common element of the set of solutions of the generalized equilibrium problems, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of the variational inequality problems for a relaxed u, v cocoercive and ξ-Lipschitz continuous mapping in a real Hilbert space. Then, we prove the strong convergence o...

In this paper, we propose and analyze a hybrid iterative method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inequality problem, and the set of fixed points of a relatively nonexpansive mapping in a real Banach space. Further, we prove the strong convergence of the sequences generated by the iterative scheme. Fi...

In this paper, we introduce a new approach method to find a common element in the intersection of the set of the solutions of a finite family of equilibrium problems and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Under appropriate conditions, some strong convergence theorems are established. The results obtained in this paper are new, and a few examples illustrat...

In this paper, we introduce the concept of generalized orthogonal F -Suzuki contraction mapping and prove some fixed point theorems on id="M2"> b -metric spaces. Our results generalize extend well-known in existing literature. As an application our results, show existence a unique solution first-order ordinary d...

generalized resolvent equations; variational inclusions; algorithm; convergence; generalized pseudocontractive mapping

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In this paper, we introduce some new iteration methods based on the hybrid method in mathematical programming, the Mann’s iterative method and the Halpern’s method for finding a fixed point of a nonexpansive mapping and a common fixed point of a nonexpansive semigroup Hilbert spaces. Mathematics Subject Classification: 41A65, 47H17, 47H20

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 Ban...

let $x$ be a reflexive banach space, $t:xto x$ be a nonexpansive mapping with $c=fix(t)neqemptyset$ and $f:xto x$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. in this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences t...

Compared with the previous work, the aim of  this paper is to introduce the more general concept of the generalized $F$-Suzuki type contraction mappings in $b$-metric spaces, and to establish some fixed point theorems in the setting of $b$-metric spaces. Our main results unify, complement and generalize the previous works in the existing literature.