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In this paper, we introduce two new types of monotone multi-valued mappings in partially ordered metric spaces and prove some fixed point theorems of those two types of mappings under some contraction conditio...
In this paper, we discuss the connection between concepts of robustness for multi-objective optimization problems and set order relations. We extend some of the existing concepts to general spaces and cones us...
In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a mixed equilibrium problem, a general system of variational inequalities and a fixed point problem of inf...
The purpose of this paper is to introduce and study a new class of nonlinear mixed ordered inclusion problems in ordered Banach spaces and to obtain an existence theorem and a comparability theorem of the reso...
The split common fixed point problem is an inverse problem that consists in finding an element in a fixed point set such that its image under a bounded linear operator belongs to another fixed point set. Recen...
In this paper, we present a new iterative scheme to solve the problems of finding common zeros of finite m-accretive mappings in a real Hilbert space. Some strong and weak convergence theorems are established und...
Convergence theorems are established in a hyperbolic space for the modified Noor iterations with errors of asymptotically nonexpansive mappings. The obtained results extend and improve the several known result...
In this paper, employing a new concept of generalized compatibility of a pair of mappings defined on a product space, certain coupled coincidence point results of mappings involved herein are obtained. We also...
In this paper, we propose and analyze an explicit type algorithm for finding a common element of the set of solutions of a finite family of generalized equilibrium problems and the set of common fixed points o...
Variational inequality problems over fixed point sets of nonexpansive mappings include many practical problems in engineering and applied mathematics, and a number of iterative methods have been presented to s...
The purpose of this paper is to obtain best proximity point theorems for a weakly contractive mapping and a weakly Kannan mapping in partial metric spaces. In this paper, the P-operator technique, which changes a...
We introduce a new nonlinear mapping similar to the nonspreading mapping which is defined by Kohsaka and Takahashi (Arch. Math. 91:166-177, 2008). We prove fixed point theorems for such a mapping without the c...
We obtain a fixed point theorem for generalized contractions on complete quasi-metric spaces, which involves w-distances and functions of Meir-Keeler and Jachymski type. Our result generalizes in various directio...
A new convex feasibility problem, the split equality problem (SEP), has been proposed by Moudafi and Byrne. The SEP was solved through the ACQA and ARCQA algorithms. In this paper the SEPs are extended to infi...
The existence of fixed points of single-valued mappings in modular function spaces has been studied by many authors. The approximation of fixed points in such spaces via convergence of an iterative process for...
In this paper, we propose an algorithms for finding a common fixed point of an infinite family of multi-valued generalized nonexpansive mappings in uniformly convex Banach spaces. Under suitable conditions some s...
In this paper, we present relaxed and composite viscosity methods for computing a common solution of a general systems of variational inequalities, common fixed points of infinitely many nonexpansive mappings ...
In this paper, we establish a general result on spherical maxima sharing the same Lagrange multiplier of which the following is a particular consequence: Let X be a real Hilbert space. For each
In this paper, the existence and the uniqueness of a common fixed point for two self-mappings satisfying some generalized Berinde-type contractions which involve an altering distance function with
In this paper, we suggest and analyze a modified projection method for finding a common solution of a system of variational inequalities, a split equilibrium problem, and a hierarchical fixed-point problem in ...
In this paper, we first study a hierarchical problem of Baillon’s type, and we study a strong convergence theorem of this problem. For the special case of this convergence theorem, we obtain a strong convergen...
We study the viscosity approximation method due to Moudafi for a fixed point problem of quasinonexpansive mappings in a Hilbert space. First, we establish a strong convergence theorem for a sequence of quasino...
Using Cesàro means of a mapping, we modify the progress of Mann’s iteration in hybrid method for asymptotically nonexpansive mappings in Hilbert spaces. Under suitable conditions, we prove that the iterative s...
The purpose of this article is to study the weak- and strong-convergence theorems of solutions to split a feasibility problem for a family of nonspreading-type mapping in Hilbert spaces. The main result presen...
The conceptions of (generalized) Tykhonov well-posedness for generalized vector quasi-equilibrium problems, (generalized) Hadamard well-posedness for parametrically generalized vector quasi-equilibrium problem...
We first introduce the concept of a triangular 2-α-η-admissible mapping which extends the notion of α-admissible mapping with respect to η to 2-metric spaces. Next, we introduce the concepts of modified weak and ...
The purpose of this paper is to prove the strong convergence of the Ishikawa iteration processes for some generalized multivalued nonexpansive mappings in the framework of CAT(1) spaces. Our results extend the...
In this paper, we first consider a split variational inclusion problem and give several strong convergence theorems in Hilbert spaces, like the Halpern-Mann type iteration method and the regularized iteration ...
We discuss the existence of a fixed point for a class of nonlinear operators in Hilbert spaces with lattice structure by a combination of variational and partial ordered methods. An application to second-order...
In this paper, we introduce an iterative process which converges strongly to a common solution of a finite family of variational inequality problems for monotone mappings with Bregman distance function. Our co...
In this paper, we study generalized strong vector quasi-equilibrium problems in topological vector spaces. Using the generalization of Fan-Browder fixed point theorem, we provide existence theorems for an exte...
Based on the concept of conjugate and biconjugate maps introduced in (Tan and Tinh in Acta Math. Viet. 25:315-345, 2000) we establish a full generalization of the Fenchel-Moreau theorem for the vector case. Be...
Based on level sets of fuzzy sets, we propose definitions of limits of sequences of fuzzy sets, and limits and derivatives of fuzzy set-valued mappings. Then, their properties are derived. Limits of sequences ...
In this paper, we first introduce a new hybrid iteration method for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces, and then we discuss the strong and weak c...
We propose a new approach to study variational relation problems. Namely, we apply Mizoguchi and Takahashi’s fixed point theorem of contraction mappings and an error bound of a system of linear inequalities to...
Recently, Iemoto and Takahashi considered a weak convergence iterative scheme for a nonspreading mapping and a nonexpansive mapping in Hilbert spaces. In this paper, we suggest two hybrid iterative algorithms ...
The purpose of this paper is to deal with the problem of finding hierarchically acommon fixed point of a sequence of nearly nonexpansive self-mappings defined ona closed convex subset of a real Hilbert space w...
In this paper, we prove strong convergence theorems to a point which is a fixed point of multi-valued mappings, a zero of an α-inverse-strongly monotone operator and a solution of the equilibrium problem. Next, w...
In the present paper, we study Newton’s method on Lie groups (independent of affine connections) for finding zeros of a mapping f from a Lie group to its Lie algebra. Under a generalized L-average Lipschitz condi...
In this paper, we consider a variational inequality problem which is defined over the set of intersections of the set of fixed points of a ζ-strictly pseudocontractive mapping, the set of fixed points of a nonexp...
We introduce new implicit and explicit iterative schemes for finding a common element of the set of fixed points of k-strictly pseudocontractive mapping and the set of zeros of the sum of two monotone operators i...
We present some total Lagrange duality results for inequality systems involving infinitely many DC functions. By using properties of the subdifferentials of involved functions, we introduce some new notions of...
The purpose of this paper is to characterize the conditions for the convergence of the iterative scheme in the sense of Agarwal et al. (J. Nonlinear Convex. Anal. 8(1): 61-79, 2007), associated with nonexpansive ...
Let C be a closed and convex subset of a real Hilbert space H. Let T be a 2-generalized hybrid mapping of C into itself, let A be an α-inverse strongly-monotone mapping of C into H, and let B and F be maximal mon...