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Relevant bibliographies by topics / Weakly sequentially continuous duality mapping

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Journal articles

Academic literature on the topic 'Weakly sequentially continuous duality mapping'

Author: Grafiati

Published: 3 June 2025

Last updated: 6 July 2025

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

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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