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Journal articles on the topic 'Reflexive Banach spaces'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Aron, Richard M., and Seán Dineen. "$Q$-Reflexive Banach Spaces." Rocky Mountain Journal of Mathematics 27, no. 4 (1997): 1009–25. http://dx.doi.org/10.1216/rmjm/1181071856.

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2

Wang, Xianfu. "Extremal characterizations of reflexive spaces." Journal of the Australian Mathematical Society 82, no. 3 (2007): 429–40. http://dx.doi.org/10.1017/s144678870003620x.

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AbstractAssume that a Banach space has a Fréchet differentiable and locally uniformly convex norm. We show that the reflexive property of the Banach space is not only sufficient, but also a necessary condition for the fulfillment of the proximal extremal principle in nonsmooth analysis.

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3

Pang, Chin-Tzong, and Eskandar Naraghirad. "Approximating Common Fixed Points of Bregman Weakly Relatively Nonexpansive Mappings in Banach Spaces." Journal of Function Spaces 2014 (2014): 1–19. http://dx.doi.org/10.1155/2014/743279.

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Using Bregman functions, we introduce a new hybrid iterative scheme for finding common fixed points of an infinite family of Bregman weakly relatively nonexpansive mappings in Banach spaces. We prove a strong convergence theorem for the sequence produced by the method. No closedness assumption is imposed on a mappingT:C→C, whereCis a closed and convex subset of a reflexive Banach spaceE. Furthermore, we apply our method to solve a system of equilibrium problems in reflexive Banach spaces. Some application of our results to the problem of finding a minimizer of a continuously Fréchet differenti

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4

Jiménez-Melado, A. "Stability of weak normal structure in James quasi reflexive space." Bulletin of the Australian Mathematical Society 46, no. 3 (1992): 367–72. http://dx.doi.org/10.1017/s0004972700012016.

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We introduce a coefficient on general Banach spaces which allows us to derive the weak normal structure for those Banach spaces whose Banach-Mazur distance to James quasi reflexive space is less than .

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5

Ghoussoub, N., B. Maurey, and W. Schachermayer. "Slicings, Selections and Their Applications." Canadian Journal of Mathematics 44, no. 3 (1992): 483–504. http://dx.doi.org/10.4153/cjm-1992-031-6.

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In the past few years, much progress have been made on several open problems in infinite dimensional Banach space theory. Here are some of the most recent results:1)The existence of boundedly complete basic sequences in a large class of Banach spaces including the ones with the so-called Radon-Nikodym property ([G-M2], [G-M4]).2)The embedding of separable reflexive Banach spaces into reflexive spaces with basis (fZl).3)The existence of long sequences of projections and hence of locally uniformly convex norms in the duals of Asplund spaces. ([F-G])

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6

Iovino, José. "Stable models and reflexive banach spaces." Journal of Symbolic Logic 64, no. 4 (1999): 1595–600. http://dx.doi.org/10.2307/2586800.

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AbstractWe show that a formula φ(x, y) is stable if and only if φ is the pairing map on the unit ball of E × E*, where E is a reflexive Banach space. The result remains true if the formula φ is replaced by a set of formulas .

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7

Couchouron, Jean-François, and P. Ligarius. "Nonlinear observers in reflexive Banach spaces." ESAIM: Control, Optimisation and Calculus of Variations 9 (January 2003): 67–103. http://dx.doi.org/10.1051/cocv:2003001.

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8

Gutev, Valentin, and Stoyan Nedev. "Continuous selections and reflexive Banach spaces." Proceedings of the American Mathematical Society 129, no. 6 (2000): 1853–60. http://dx.doi.org/10.1090/s0002-9939-00-05740-3.

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9

Matoušková, Eva, and Charles Stegall. "A characterization of reflexive Banach spaces." Proceedings of the American Mathematical Society 124, no. 4 (1996): 1083–90. http://dx.doi.org/10.1090/s0002-9939-96-03093-6.

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10

Harder, Felix. "Legendre Forms in Reflexive Banach Spaces." Zeitschrift für Analysis und ihre Anwendungen 37, no. 4 (2018): 377–88. http://dx.doi.org/10.4171/zaa/1619.

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11

Merlevède, Florence, Costel Peligrad, and Magda Peligrad. "Reflexive operator algebras on Banach spaces." Pacific Journal of Mathematics 267, no. 2 (2014): 451–64. http://dx.doi.org/10.2140/pjm.2014.267.451.

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12

Suslov, S. I. "Fatou's Lemma in Reflexive Banach Spaces." Journal of Mathematical Analysis and Applications 199, no. 3 (1996): 748–53. http://dx.doi.org/10.1006/jmaa.1996.0172.

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13

Venkova, M. "Properties of Q-Reflexive Banach Spaces." Journal of Mathematical Analysis and Applications 264, no. 1 (2001): 96–106. http://dx.doi.org/10.1006/jmaa.2001.7644.

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14

Chen, Quanyuan, and Xiaochun Fang. "Strictly Cyclic Functionals, Reflexivity, and Hereditary Reflexivity of Operator Algebras." Abstract and Applied Analysis 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/434308.

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This paper is concerned with strictly cyclic functionals of operator algebras on Banach spaces. It is shown that ifXis a reflexive Banach space andAis a norm-closed semisimple abelian subalgebra ofB(X)with a strictly cyclic functionalf∈X∗, thenAis reflexive and hereditarily reflexive. Moreover, we construct a semisimple abelian operator algebra having a strictly cyclic functional but having no strictly cyclic vectors. The hereditary reflexivity of an algbra of this type can follow from theorems in this paper, but does not follow directly from the known theorems that, if a strictly cyclic opera

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15

HONG, SUK-JOON, and IN-SOOK KIM. "Some surjectivity results for operators of generalized monotone type via a topological degree." Carpathian Journal of Mathematics 34, no. 3 (2018): 333–40. http://dx.doi.org/10.37193/cjm.2018.03.07.

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We introduce a topological degree for a class of operators of generalized monotone type in reflexive Banach spaces, based on the recent Berkovits degree. Using the degree theory, we give some surjectivity results for operators of generalized monotone type in reflexive Banach spaces. In the Hilbert space case, this reduces to the celebrated Browder-Minty theorem for monotone operators.

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16

Borwein, Jonathan M., and Simon Fitzpatrick. "Existence Of Nearest Points In Banach Spaces." Canadian Journal of Mathematics 41, no. 4 (1989): 702–20. http://dx.doi.org/10.4153/cjm-1989-032-7.

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This paper makes a unified development of what the authors know about the existence of nearest points to closed subsets of (real) Banach spaces. Our work is made simpler by the methodical use of subderivatives. The results of Section 3 and Section 7 in particular are, to the best of our knowledge, new. In Section 5 and Section 6 we provide refined proofs of the Lau-Konjagin nearest point characterizations of reflexive Kadec spaces (Theorem 5.11, Theorem 6.6) and give a substantial extension (Theorem 5.12). The main open question is: are nearest points dense in the boundary of every closed subs

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17

Ajeti, Laura, Atanas Ilchev, and Boyan Zlatanov. "On Coupled Best Proximity Points in Reflexive Banach Spaces." Mathematics 10, no. 8 (2022): 1304. http://dx.doi.org/10.3390/math10081304.

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We investigated the existence and uniqueness of coupled best proximity points for some cyclic and semi-cyclic maps in a reflexive Banach space. We found sufficient conditions, ensuring the existence of coupled best proximity points in reflexive Banach spaces and some convexity types of conditions, ensuring uniqueness of the coupled best proximity points in strictly convex Banach spaces. We illustrate the results with examples and we present an application of one of the theorems in the modeling of duopoly markets, to have an existence of market equilibrium. We show that, in general, the iterati

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18

Taskovic, Milan. "Diametral contractive mappings in reflexive banach spaces." Mathematica Moravica, no. 6 (2002): 103–8. http://dx.doi.org/10.5937/matmor0206103t.

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19

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

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20

Naniewicz, Zdzisław. "Economic equilibrium problems in reflexive Banach spaces." Nonlinear Analysis: Theory, Methods & Applications 65, no. 10 (2006): 1925–54. http://dx.doi.org/10.1016/j.na.2005.11.001.

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21

Bounkhel, M., and R. Al-Yusof. "Proximal analysis in reflexive smooth Banach spaces." Nonlinear Analysis: Theory, Methods & Applications 73, no. 7 (2010): 1921–39. http://dx.doi.org/10.1016/j.na.2010.04.077.

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22

Barcenas, Diomedes, and Joe Diestel. "CONSTRAINED CONTROLLABILITY IN NON REFLEXIVE BANACH SPACES." Quaestiones Mathematicae 18, no. 1-3 (1995): 185–98. http://dx.doi.org/10.1080/16073606.1995.9631794.

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23

Cardinali, Tiziana, and Nikolaos S. Papageorgiou. "Hammerstein integral inclusions in reflexive Banach spaces." Proceedings of the American Mathematical Society 127, no. 1 (1999): 95–103. http://dx.doi.org/10.1090/s0002-9939-99-04906-0.

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24

Trudzik, L. I. "Perturbed convex programming in reflexive Banach spaces." Nonlinear Analysis: Theory, Methods & Applications 9, no. 1 (1985): 61–78. http://dx.doi.org/10.1016/0362-546x(85)90053-7.

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25

Prus-Wiśniowski, Franciszek, та William H. Ruckle. "The Banach spaces ΛBV are non-reflexive". Journal of Mathematical Analysis and Applications 389, № 2 (2012): 1394–96. http://dx.doi.org/10.1016/j.jmaa.2011.11.040.

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26

Bridges, Douglas S., Hajime Ishihara, and Maarten McKubre-Jordens. "Uniformly convex Banach spaces are reflexive-constructively." Mathematical Logic Quarterly 59, no. 4-5 (2013): 352–56. http://dx.doi.org/10.1002/malq.201200093.

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27

Qiu, Jing Hui. "A Cone Characterization of Reflexive Banach Spaces." Journal of Mathematical Analysis and Applications 256, no. 1 (2001): 39–44. http://dx.doi.org/10.1006/jmaa.2000.7253.

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28

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

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29

Zhao, Yali, Zunquan Xia, and Zeqing Liu. "Generalized set-valued variational-like inclusions and Wiener-Hopf equations in Banach spaces." International Journal of Mathematics and Mathematical Sciences 2005, no. 22 (2005): 3645–59. http://dx.doi.org/10.1155/ijmms.2005.3645.

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By using the notion ofJη-proximal mapping for a nonconvex, lower semicontinuous,η-subdifferentiable proper functional in reflexive Banach spaces, we introduce and study a class of generalized set-valued variational-like inclusions in Banach spaces and show their equivalences with a class of Wiener-Hopf equations. We propose two new iterative algorithms for the class of generalized set-valued variational-like inclusions. Furthermore, we prove the existence of solutions of the generalized set-valued variational-like inclusions and the convergence criteria of the two iterative algorithms for the

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30

Seddighi, K., K. Hedayatiyan, and B. Yousefi. "Operators acting on certain Banach spaces of analytic functions." International Journal of Mathematics and Mathematical Sciences 18, no. 1 (1995): 107–10. http://dx.doi.org/10.1155/s0161171295000147.

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Let𝒳be reflexive Banach space of functions analytic plane domainΩsuch that for everyλinΩthe functional of evaluation atλis bounded. Assume further that𝒳contains the constants andMzmultiplication by the independent variablez, is bounded operator on𝒳. We give sufficient conditions forMzto be reflexive. In particular, we prove that the operatorsMzonEP(Ω)and certainHaP(β)reflexive. We also prove that the algebra of multiplication operators on Bergman spaces is reflexive, giving simpler proof of result of Eschmeier.

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31

Kamińska, Anna, and Han Ju Lee. "The Banach-Saks Properties in Orlicz-Lorentz Spaces." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/423198.

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The Banach-Saks index of an Orlicz-Lorentz spaceΛφ,w(I)for both function and sequence case, is computed with respect to its Matuszewska-Orlicz indices ofφ. It is also shown that an Orlicz-Lorentz function space has weak Banach-Saks (resp., Banach-Saks) property if and only if it is separable (resp., reflexive).

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32

Pang, Chin-Tzong, Eskandar Naraghirad, and Ching-Feng Wen. "Bregmanf-Projection Operator with Applications to Variational Inequalities in Banach Spaces." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/594285.

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Using Bregman functions, we introduce the new concept of Bregman generalizedf-projection operatorProjCf, g:E*→C, whereEis a reflexive Banach space with dual spaceE*; f: E→ℝ∪+∞is a proper, convex, lower semicontinuous and bounded from below function;g: E→ℝis a strictly convex and Gâteaux differentiable function; andCis a nonempty, closed, and convex subset ofE. The existence of a solution for a class of variational inequalities in Banach spaces is presented.

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33

BELAY, YIRGA ABEBE, HABTU ZEGEYE, and OGANEDITSE A. BOIKANYO. ""Solutions of Split Equality Hammerstein Type Equation Problems in Reflexive Real Banach Spaces"." Carpathian Journal of Mathematics 39, no. 1 (2022): 45–72. http://dx.doi.org/10.37193/cjm.2023.01.03.

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"The purpose of this study is to introduce an inertial algorithm for approximating a solution of the split equality Hammerstein type equation problem in general reflexive real Banach spaces. Strong convergence results are established under the assumption that the associated mappings are monotone and uniformly continuous. The results in this paper generalize and improve many of the existing results in the literature in the sense that the underlying mappings are relaxed from Lipschitz continuous to uniformly continuous and the spaces under consideration are extended from Hilbert spaces to reflex

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34

Zegeye, H., and N. Shahzad. "Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/584395.

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We prove a strong convergence theorem for a common fixed point of a finite family of right Bregman strongly nonexpansive mappings in the framework of real reflexive Banach spaces. Furthermore, we apply our method to approximate a common zero of a finite family of maximal monotone mappings and a solution of a finite family of convex feasibility problems in reflexive real Banach spaces. Our theorems complement some recent results that have been proved for this important class of nonlinear mappings.

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35

El-Shobaky, Entisarat, Sahar Mohammed Ali, and Wataru Takahashi. "On projection constant problems and the existence of metric projections in normed spaces." Abstract and Applied Analysis 6, no. 7 (2001): 401–11. http://dx.doi.org/10.1155/s1085337501000732.

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We give the sufficient conditions for the existence of a metric projection onto convex closed subsets of normed linear spaces which are reduced conditions than that in the case of reflexive Banach spaces and we find a general formula for the projections onto the maximal proper subspaces of the classical Banach spacesl p,1≤p<∞andc 0. We also give the sufficient and necessary conditions for an infinite matrix to represent a projection operator froml p,1≤p<∞orc 0onto anyone of their maximal proper subspaces.

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36

Cho, Chong-Man. "Spaces of compact operators which areM-ideals inL(X,Y)." International Journal of Mathematics and Mathematical Sciences 15, no. 3 (1992): 617–19. http://dx.doi.org/10.1155/s0161171292000802.

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SupposeXandYare reflexive Banach spaces. IfK(X,Y), the space of all compact linear operaters fromXtoYis anM-ideal inL(X,Y), the space of all bounded linear operators fromXtoY, then the second dual spaceK(X,Y)**ofK(X,Y)is isometrically isomorphic toL(X,Y).

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37

Ndoutoume, James Louis, and Michel Théra. "Generalised second-order derivatives of convex functions in reflexive Banach spaces." Bulletin of the Australian Mathematical Society 51, no. 1 (1995): 55–72. http://dx.doi.org/10.1017/s0004972700013897.

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Generalised second-order derivatives introduced by Rockafellar in the finite dimensional setting are extended to convex functions defined on reflexive Banach spaces. Our approach is based on the characterisation of convex generalised quadratic forms defined in reflexive Banach spaces, from the graph of the associated subdifferentials. The main result which is obtained is the exhibition of a particular generalised Hessian when the function admits a generalised second derivative. Some properties of the generalised second derivative are pointed out along with further justifications of the concept

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38

Bounkhel, Messaoud, and Mostafa Bachar. "Primal Lower Nice Functions in Reflexive Smooth Banach Spaces." Mathematics 8, no. 11 (2020): 2066. http://dx.doi.org/10.3390/math8112066.

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In the present work, we extend, to the setting of reflexive smooth Banach spaces, the class of primal lower nice functions, which was proposed, for the first time, in finite dimensional spaces in [Nonlinear Anal. 1991, 17, 385–398] and enlarged to Hilbert spaces in [Trans. Am. Math. Soc. 1995, 347, 1269–1294]. Our principal target is to extend some existing characterisations of this class to our Banach space setting and to study the relationship between this concept and the generalised V-prox-regularity of the epigraphs in the sense proposed recently by the authors in [J. Math. Anal. Appl. 201

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39

Jolaoso, Lateef Olakunle, Ferdinard Udochukwu Ogbuisi, and Oluwatosin Temitope Mewomo. "An iterative method for solving minimization, variational inequality and fixed point problems in reflexive Banach spaces." Advances in Pure and Applied Mathematics 9, no. 3 (2018): 167–84. http://dx.doi.org/10.1515/apam-2017-0037.

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Abstract In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is also a solution to finite systems of convex minimization problems and variational inequality problems in real reflexive Banach spaces. We obtain a strong convergence result and give applications of our result to finding zeroes of an infinite family of Bregman inverse strongly monotone operators and a finite system of equilibrium problems in real reflexive Banach spaces. Our result extends many recent corresponding results in lite

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40

Chen, Quanyuan, and Xiaochun Fang. "Spatiality of Derivations of Operator Algebras in Banach Spaces." Abstract and Applied Analysis 2011 (2011): 1–13. http://dx.doi.org/10.1155/2011/813723.

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Suppose thatAis a transitive subalgebra ofB(X)and its norm closureA¯contains a nonzero minimal left idealI. It is shown that ifδis a bounded reflexive transitive derivation fromAintoB(X), thenδis spatial and implemented uniquely; that is, there existsT∈B(X)such thatδ(A)=TA−ATfor eachA∈A, and the implementationTofδis unique only up to an additive constant. This extends a result of E. Kissin that “ifA¯contains the idealC(H)of all compact operators inB(H), then a bounded reflexive transitive derivation fromAintoB(H)is spatial and implemented uniquely.” in an algebraic direction and provides an al

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41

Castillo, J. M. F., and F. Sanchez. "Weakly p-Compact, p-Banach-Saks, and Super-reflexive Banach Spaces." Journal of Mathematical Analysis and Applications 185, no. 2 (1994): 256–61. http://dx.doi.org/10.1006/jmaa.1994.1246.

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42

Khademzadeh, H. R., and H. Mazaheri. "Monotonicity and the Dominated Farthest Points Problem in Banach Lattice." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/616989.

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We introduce the dominated farthest points problem in Banach lattices. We prove that for two equivalent norms such thatXbecomes an STM and LLUM space the dominated farthest points problem has the same solution. We give some conditions such that under these conditions the Fréchet differentiability of the farthest point map is equivalent to the continuity of metric antiprojection in the dominated farthest points problem. Also we prove that these conditions are equivalent to strong solvability of the dominated farthest points problem. We prove these results in STM, reflexive STM, and UM spaces. M

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43

Hassan, Ezzat R., M. Sh Alhuthali, and M. M. Al-Ghanmi. "Generalized Uniqueness Theorem for Ordinary Differential Equations in Banach Spaces." Scientific World Journal 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/272479.

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We consider nonlinear ordinary differential equations in Banach spaces. Uniqueness criterion for the Cauchy problem is given when any of the standard dissipative-type conditions does apply. A similar scalar result has been studied by Majorana (1991). Useful examples of reflexive Banach spaces whose positive cones have empty interior has been given as well.

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44

Ferenczi, V. "Quotient Hereditarily Indecomposable Banach Spaces." Canadian Journal of Mathematics 51, no. 3 (1999): 566–84. http://dx.doi.org/10.4153/cjm-1999-026-4.

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AbstractA Banach space X is said to be quotient hereditarily indecomposable if no infinite dimensional quotient of a subspace of X is decomposable. We provide an example of a quotient hereditarily indecomposable space, namely the space XGM constructed by W. T. Gowers and B. Maurey in [GM]. Then we provide an example of a reflexive hereditarily indecomposable space whose dual is not hereditarily indecomposable; so is not quotient hereditarily indecomposable. We also show that every operator on * is a strictly singular perturbation of an homothetic map.

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45

Cuenya, H. H., and F. E. Levis. "Existence of optimal subspaces in reflexive Banach spaces." Annals of Functional Analysis 6, no. 2 (2015): 69–77. http://dx.doi.org/10.15352/afa/06-2-7.

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46

Shtern, A. I. "Triviality Theorem for Quasirepresentations in Reflexive Banach Spaces." Russian Journal of Mathematical Physics 29, no. 3 (2022): 397–401. http://dx.doi.org/10.1134/s1061920822030074.

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47

Taskovic, Milan. "Characterization of reflexive banach spaces with normal structure." Mathematica Moravica, no. 6 (2002): 97–102. http://dx.doi.org/10.5937/matmor0206097t.

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48

Bounkhel, Messaoud. "Implicit differential inclusions in reflexive smooth Banach spaces." Proceedings of the American Mathematical Society 140, no. 8 (2012): 2767–82. http://dx.doi.org/10.1090/s0002-9939-2011-11122-5.

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49

Avgerinos, Evgenios P., and Nikolaos S. Papageorgiou. "Random nonlinear evolution inclusions in reflexive Banach spaces." Proceedings of the American Mathematical Society 104, no. 1 (1988): 293. http://dx.doi.org/10.1090/s0002-9939-1988-0958086-6.

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50

Graham, Ian, Hidetaka Hamada, Gabriela Kohr, and Mirela Kohr. "Asymptotically Spirallike Mappings in Reflexive Complex Banach Spaces." Complex Analysis and Operator Theory 7, no. 6 (2012): 1909–27. http://dx.doi.org/10.1007/s11785-012-0273-3.

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