• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.251-263
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• 1993

The purpose of this paper is to study the solvability of the equation (E). In Section 2, we give preliminary definitions. In Section 3, we prove related two results (Theorem 1 and Corollary 1) concerning the closedness property of accretive operators in the class of spaces whose nonempty bounded closed convex subsets have the fixed point property for nonexpansive self-mapping. Using therem 1, we derive a result (Theorem 2) on the range of accetive operators in (.pi.)$_{1}$ spaces with a view to establishing a new result, which improves a result of Kartsatos [8] and Webb [15]. Further, we give an interesting consequence (Corollary 3) of Theorem 2. In section 4, we apply Corollary 1 to obtain two results (Theorem 3 and 4) for the range of sums of two accretive operators, which generalize two results of Reich [12].

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.411-432
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• 2021

In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.433-442
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• 2021

Let X and X^* be a Banach space and its dual, respectively, and let B(X) and S(X) be the unit ball and unit sphere of X, respectively. In this paper, we study the relation between Modulus of n-dimensional U-convexity in X^* and normal structure in X. Some new results about fixed points of nonexpansive mapping are obtained, and some existing results are improved. Among other results, we proved: if X is a Banach space with $U^n_{X^*}(n+1)>1-{\frac{1}{n+1}}$ where n ∈ ℕ, then X has weak normal structure.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.203-221
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• 2022

In this paper, we introduce new hybrid inertial contraction projection algorithms for solving variational inequality problems over the intersection of the fixed point sets of demicontractive mappings in a real Hilbert space. The proposed algorithms are based on the hybrid steepest-descent method for variational inequality problems and the inertial techniques for finding fixed points of nonexpansive mappings. Strong convergence of the iterative algorithms is proved. Several fundamental experiments are provided to illustrate computational efficiency of the given algorithm and comparison with other known algorithms

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.995-1009
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• 2021

Many iterative algorithms like that Picard, Mann, Ishikawa and S-iteration are very useful to elucidate the fixed point problems of a nonlinear operators in various topological spaces. The recent trend for elucidate the fixed point via inertial iterative algorithm, in which next iterative depends on more than one previous terms. The purpose of the paper is to establish convergence theorems of new inertial Picard normal S-iteration algorithm for nonexpansive mapping in Hilbert spaces. The comparison of convergence of InerNSP and InerPNSP is done with InerSP (introduced by Phon-on et al. [25]) and MSP (introduced by Suparatulatorn et al. [27]) via numerical example.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.175-203
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• 2023

In this paper, we study an iterative algorithm that is based on inertial proximal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on prediction stepsize conditions, and under some standard assumptions on the algorithm parameters. Finally, some special cases of general problem are given as applications. Our results improve and generalized some well-known and related results in literature.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.69-94
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• 2024

In this paper, we introduce an inertial self-adaptive projection method using Bregman distance techniques for solving pseudomonotone equilibrium problems in reflexive Banach spaces. The algorithm requires only one projection onto the feasible set without any Lipschitz-like condition on the bifunction. Using this method, a strong convergence theorem is proved under some mild conditions. Furthermore, we include numerical experiments to illustrate the behaviour of the new algorithm with respect to the Bregman function and other algorithms in the literature.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.393-418
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• 2024

In this paper, we propose a new inertial subgradient extragradient algorithm with a new linesearch technique that combines the inertial subgradient extragradient algorithm and the KrasnoselskiiMann algorithm. Under some suitable conditions, we prove a weak convergence theorem of the proposed algorithm for finding a common element of the common solution set of a finitely many variational inequality problem and the fixed point set of a nonexpansive mapping in real Hilbert spaces. Moreover, using our main result, we derive some others involving systems of variational inequalities. Finally, we give some numerical examples to support our main result.