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Journal articles on the topic 'Weakly sequentially continuous duality mapping'

Author: Grafiati

Published: 3 June 2025

Last updated: 6 July 2025

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1

K., Piesie Frimpong, and Prempeh E. "Viscosity Approximation Methods in Re exive Banach Spaces with a Sequence of Contractions." British Journal of Mathematics & Computer Science 22, no. 3 (2017): 1–10. https://doi.org/10.9734/BJMCS/2017/33414.

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The aim of this paper is to study viscosity approximation methods in re exive Banach spaces. Let E be a re exive Banach space which admits a weakly sequentially continuous duality mapping j : E → E , C a nonempty closed convex subset of E, μn, n ≥ 1 a sequence of contractions on C and Tn, n = 1, 2, 3, · · ·N a nite family of nonexpansive mappings on C. We show that under appropriate conditions on κ the implicit iterative sequence τ de ned by τ = κμn(τ) + (1 − κ)Tnτ where κ ∈ (0, 1) converges strongly to a common xed point τ ∈ k∩ n=1 FTn. We further show that the results hold for an in nite family Tn, n ∈ N of nonexpansive mappings.

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2

Shehu, Yekini, and Jerry N. Ezeora. "Path Convergence and Approximation of Common Zeroes of a Finite Family ofm-Accretive Mappings in Banach Spaces." Abstract and Applied Analysis 2010 (2010): 1–14. http://dx.doi.org/10.1155/2010/285376.

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LetEbe a real Banach space which is uniformly smooth and uniformly convex. LetKbe a nonempty, closed, and convex sunny nonexpansive retract ofE, whereQis the sunny nonexpansive retraction. IfEadmits weakly sequentially continuous duality mappingj, path convergence is proved for a nonexpansive mappingT:K→K. As an application, we prove strong convergence theorem for common zeroes of a finite family ofm-accretive mappings ofKtoE. As a consequence, an iterative scheme is constructed to converge to a common fixed point (assuming existence) of a finite family of pseudocontractive mappings fromKtoEunder certain mild conditions.

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3

K., Piesie Frimpong, and Prempeh E. "Viscosity Approximation Methods in Reflexive Banach Spaces." British Journal of Mathematics & Computer Science 22, no. 2 (2017): 1–11. https://doi.org/10.9734/BJMCS/2017/33396.

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In this paper, we study viscosity approximation methods in reflexive Banach spaces. Let X be a reflexive Banach space which admits a weakly sequentially continuous duality mapping <em>j : X → X<sup>*</sup>, C</em> a nonempty closed convex subset of <em>X, h<sub>n</sub></em>, where n ≥1 a sequence of contractions on C and Tn, n = 1; 2; 3; N, for N 2 N, a nite family of commuting nonexpansive mappings on C. We show that under appropriate conditions on n the explicit iterative sequence n de ned by n+1 = nhn(n) + (1 􀀀 n)Tnn; n 1; 1 2 C where n 2 (0; 1) converges strongly to a common xed point 2 NT k=1 Fk : We consequently show that the results is true for an in nite family Tn; n = 1; 2; 3; of commuting nonexpansive mapping on C.

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4

Wangkeeree, Rattanaporn. "Strong Convergence Theorems of the General Iterative Methods for Nonexpansive Semigroups in Banach Spaces." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–21. http://dx.doi.org/10.1155/2011/643740.

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LetEbe a real reflexive Banach space which admits a weakly sequentially continuous duality mapping fromEtoE*. LetS={T(s):0≤s<∞}be a nonexpansive semigroup onEsuch thatFix(S):=⋂t≥0Fix(T(t))≠∅, andfis a contraction onEwith coefficient0<α<1. LetFbeδ-strongly accretive andλ-strictly pseudocontractive withδ+λ>1andγa positive real number such thatγ<1/α(1-1-δ/λ). When the sequences of real numbers{αn}and{tn}satisfy some appropriate conditions, the three iterative processes given as follows:xn+1=αnγf(xn)+(I-αnF)T(tn)xn,n≥0,yn+1=αnγf(T(tn)yn)+(I-αnF)T(tn)yn,n≥0, andzn+1=T(tn)(αnγf(zn)+(I-αnF)zn),n≥0converge strongly tox̃, wherex̃is the unique solution inFix(S)of the variational inequality〈(F-γf)x̃,j(x-x̃)〉≥0,x∈Fix(S). Our results extend and improve corresponding ones of Li et al. (2009) Chen and He (2007), and many others.

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5

Jung, Jong. "Convergence of iterative algorithms for continuous pseudocontractive mappings." Filomat 30, no. 7 (2016): 1767–77. http://dx.doi.org/10.2298/fil1607767j.

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In this paper, we prove strong convergence of a path for a convex combination of a pseudocontractive type of operators in a real reflexive Banach space having a weakly continuous duality mapping J? with gauge function ?. Using path convergency, we establish strong convergence of an implicit iterative algorithm for a pseudocontractive mapping combined with a strongly pseudocontractive mapping in the same Banach space.

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6

Yue, Chen, H. M. Abu-Donia, H. A. Atia, et al. "Weakly compatible fixed point theorem in intuitionistic fuzzy metric spaces." AIP Advances 13, no. 4 (2023): 045113. http://dx.doi.org/10.1063/5.0147488.

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This study presents fundamental theorems, lemmas, and mapping definitions. There are three types of mappings: binary operators, compatible mappings, and sequentially continuous mappings. The symbols used to represent fuzzy metric spaces are intuitive. Icons were also used to prescribe a shared, linked fixed point in intuitionistic fuzzy metric space for two compatible and sequentially continuous mappings that satisfy ϕ-contractive conditions. To accomplish this, finding the intersection of both mappings was necessary.

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7

Ali, Bashir. "Common Fixed Points Approximation for Asymptotically Nonexpansive Semigroup in Banach Spaces." ISRN Mathematical Analysis 2011 (August 3, 2011): 1–14. http://dx.doi.org/10.5402/2011/684158.

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Let be a real Banach space satisfying local uniform Opial's condition, whose duality map is weakly sequentially continuous. Let be a uniformly asymptotically regular family of asymptotically nonexpansive semigroup of with function . Let and be weakly contractive map. Let be -strongly accretive and -strictly pseudocontractive map with . Let be an increasing sequence in and let and be sequences in satisfying some conditions. For some positive real number appropriately chosen, let be a sequence defined by , , , . It is proved that converges strongly to a common fixed point of the family which is also the unique solution of the variational inequality .

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8

Jung, Jong Soo. "Convergence Theorems for Modified Implicit Iterative Methods with Perturbation for Pseudocontractive Mappings." Mathematics 8, no. 1 (2020): 72. http://dx.doi.org/10.3390/math8010072.

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In this paper, first, we introduce a path for a convex combination of a pseudocontractive type of mappings with a perturbed mapping and prove strong convergence of the proposed path in a real reflexive Banach space having a weakly continuous duality mapping. Second, we propose two modified implicit iterative methods with a perturbed mapping for a continuous pseudocontractive mapping in the same Banach space. Strong convergence theorems for the proposed iterative methods are established. The results in this paper substantially develop and complement the previous well-known results in this area.

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9

Wangkeeree, Rabian, and Pakkapon Preechasilp. "The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces." Abstract and Applied Analysis 2012 (2012): 1–20. http://dx.doi.org/10.1155/2012/695183.

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We introduce the general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups which is a unique solution of some variational inequalities. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature.

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10

Sunthrayuth, Pongsakorn, and Poom Kumam. "A New Composite General Iterative Scheme for Nonexpansive Semigroups in Banach Spaces." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–18. http://dx.doi.org/10.1155/2011/560671.

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We introduce a new general composite iterative scheme for finding a common fixed point of nonexpansive semigroups in the framework of Banach spaces which admit a weakly continuous duality mapping. A strong convergence theorem of the purposed iterative approximation method is established under some certain control conditions. Our results improve and extend announced by many others.

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11

Wangkeeree, Rabian. "The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces." Abstract and Applied Analysis 2011 (2011): 1–19. http://dx.doi.org/10.1155/2011/854360.

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We introduce two general hybrid iterative approximation methods (one implicit and one explicit) for finding a fixed point of a nonexpansive mapping which solving the variational inequality generated by two strongly positive bounded linear operators. Strong convergence theorems of the proposed iterative methods are obtained in a reflexive Banach space which admits a weakly continuous duality mapping. The results presented in this paper improve and extend the corresponding results announced by Marino and Xu (2006), Wangkeeree et al. (in press), and Ceng et al. (2009).

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12

Liu, Liya, Xiaolong Qin, and Jen-Chih Yao. "Strong Convergent Theorems Governed by Pseudo-Monotone Mappings." Mathematics 8, no. 8 (2020): 1256. http://dx.doi.org/10.3390/math8081256.

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The purpose of this paper is to introduce two different kinds of iterative algorithms with inertial effects for solving variational inequalities. The iterative processes are based on the extragradient method, the Mann-type method and the viscosity method. Convergence theorems of strong convergence are established in Hilbert spaces under mild assumption that the associated mapping is Lipschitz continuous, pseudo-monotone and sequentially weakly continuous. Numerical experiments are performed to illustrate the behaviors of our proposed methods, as well as comparing them with the existing one in literature.

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13

Xu, Hong-Kun, and Luigi Muglia. "On solving variational inequalities defined on fixed point sets of multivalued mappings in Banach spaces." Journal of Fixed Point Theory and Applications 22, no. 4 (2020). http://dx.doi.org/10.1007/s11784-020-00817-1.

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AbstractWe are concerned with the problem of solving variational inequalities which are defined on the set of fixed points of a multivalued nonexpansive mapping in a reflexive Banach space. Both implicit and explicit approaches are studied. Strong convergence of the implicit method is proved if the space satisfies Opial’s condition and has a duality map weakly continuous at zero, and the strong convergence of the explicit method is proved if the space has a weakly continuous duality map. An essential assumption on the multivalued nonexpansive mapping is that the mapping be single valued on its nonempty set of fixed points.

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14

Saleh, Omran, and Elrawy A. "Continuous and bounded operators on neutrosophic normed spaces." October 7, 2021. https://doi.org/10.5281/zenodo.5553525.

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In this paper, we define the concept of continuous, sequentially continuous, and strongly continuous mappings neutrosophic normed spaces. Also, we have some important relationships between continuous, sequentially continuous, strongly continuous relationships mappings. Furthermore, the concept of neutrosophic Lipschitzian mapping is introduced and a neutrosophic version of Banach’s contraction principle is achieved. Finally, the definition of neutrosophic bounded and weakly bounded linear operators are discussed and studied.

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15

Chidume, C. "Iterative approximation of fixed points of Lipschitz pseudocontractive maps." July 26, 2002. https://doi.org/10.1090/s0002-9939-01-06078-6.

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Let E E be a q q -uniformly smooth Banach space possessing a weakly sequentially continuous duality map (e.g., ℓ p , 1 > p > ∞ \ell _p, \ 1>p>\infty ). Let T T be a Lipschitzian pseudocontractive selfmapping of a nonempty closed convex and bounded subset K K of E E and let ω ∈ K \omega \in K be arbitrary. Then the iteration sequence { z n } \{z_n\} defined by z 0 ∈ K , z n + 1 = ( 1 − μ n + 1 ) ω + μ n + 1 y n ; y n = ( 1 − α n ) z n + α n T z n z_0\in K, \ \ z_{n+1}=(1-\mu _{n+ 1})\omega + \mu _{n+1}y_n; \ \ y_n = (1-\alpha _n)z_n+\alpha _nTz_n , converges strongly to a fixed point of T T , provided that { μ n } \{\mu _n\} and { α n } \{\alpha _n\} have certain properties. If E E is a Hilbert space, then { z n } \{z_n\} converges strongly to the unique fixed point of T T closest to ω \omega .

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