Inclusion Properties of Orlicz Spaces and Weak Orlicz Spaces Generated by Concave Functions
|
|
- Hilda Whitehead
- 5 years ago
- Views:
Transcription
1 IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Inclusion Properties of Orlicz Spaces and Weak Orlicz Spaces Generated y Concave Functions To cite this article: M Taqiyuddin and A A Masta 208 IOP Conf. Ser.: Mater. Sci. Eng View the article online for updates and enhancements. This content was downloaded from IP address on 27/09/208 at 8:5
2 The 2nd Annual Applied Science and Engineering Conference (AASEC 207) IOP Pulishing IOP Conf. Series: Materials Science and Engineering (208) 0203 doi:0.088/ x/288//0203 Inclusion Properties of Orlicz Spaces and Weak Orlicz Spaces Generated y Concave Functions M Taqiyuddin and A A Masta Department of Mathematics Education, Universitas Pendidikan Indonesia, Jl. Dr. Setiaudi no. 229, Bandung 4054, Indonesia *taqi94@hotmail.com Astract. In this paper, we introduce Orlicz spaces generated y concave functions and estalish some inclusion properties etween them. In addition, we also otain similar result for weak Orlicz spaces. One of the keys to prove our result is y estimating characteristic function of open alls in R n.. Introduction and preliminaries There is an ongoing discussion on Orlicz spaces over past decades. This space was firstly introduced y Z W Birnaum and W Orlicz in 93 [] and the discussion is still going on. As one of them, in 989, Maligandra [2] studied some inclusion properties on Orlicz spaces. In 206, Masta et al. [3] also reprove some inclusion properties of Orlicz spaces and weak Orlicz spaces. Furthermore, several oservations of the inclusion properties of these spaces have een done y other researchers. Osançliol [4] has proved sufficient and necessary conditions for inclusion relation etween two weighted Orlicz spaces. Related results aout inclusion properties of Orlicz spaces can e found in [5-6]. These results have attracted us to oserve further within the inclusion properties of these spaces and their weak type. It is a convenient way to associate Orlicz spaces with convex functions (see for example [3,4,7]). However, recently, some researchers associated Orlicz spaces with concave function. In particular, Zhou et al. [8] discussed the weak Martingale Orlicz-Karamata-Hardy spaces associated with concave functions, and Zhang and Zhang [9] studied the weak Orlicz spaces associated with concave functions. Motivated y this trend, we have decided to study the inclusion properties of Orlicz spaces and weak Orlicz spaces generated y concave functions. The rest of paper is organized as follows. In this section, we will recall and give some definitions and some lemmas which will e used in our proofs. More specifically, we will give the definitions of Orlicz spaces and weak Orlicz spaces generated y concave functions in this section. Then, we will present our results in section 2. The inclusion properties will e discussed there. Throughout this paper, the letter C will e used for constants that may change from line to line, while constants with suscripts, such as C do not change in different lines. Let G e the set of all funtionsφ: [0, ) [0, ) e an increasing, ijective, continuous, and concave function satisfying Φ(0) = 0, lim t + 0 Φ(t) = 0, and lim t Φ(t) =. We denote Φ Φ 2 for Φ, Φ 2 G if there is a constant C > 0 such that Φ (t) Φ 2 (Ct) for all t 0.For Φ G, the Orlicz space generated y concave functions L Φ (R n ) is defined as follows Content from this work may e used under the terms of the Creative Commons Attriution 3.0 licence. Any further distriution of this work must maintain attriution to the author(s) and the title of the work, journal citation and DOI. Pulished under licence y IOP Pulishing Ltd
3 The 2nd Annual Applied Science and Engineering Conference (AASEC 207) IOP Pulishing IOP Conf. Series: Materials Science and Engineering (208) 0203 doi:0.088/ x/288//0203 for some > 0, and its quasi-norm is L Φ (R n ) = {f R n : Φ ( f(x) )dx < }, R n f LΦ (R n ) inf { > 0: Φ ( f(x) ) dx }. R n By using similar argument on the Orlicz spaces with convex function (see [,2,4,7,0]) we can prove that the Orlicz space generated y concave functions L Φ (R n ) is a quasi-banach space with respect to the quasi-norm f LΦ Note that, if Φ(t): = t p for some 0 < p <, then L Φ (R n ) = L p On the other hand, for Φ G, the weak Orlicz spaces generated y concave functions wl Φ (R n ) is defined as follows wl Φ (R n ) = {f R n : f wlφ < }, Where f wlφ (R n ) inf { > 0: sup Φ(t) {x R n : f(x) > t} }. Weak Orlicz space generated y concave functions wl Φ (R n ) is also a quasi-banach space with respect to the quasi-norm f LΦ (R n ) (see [9]). For Φ(t): = t p (0 < p < ), wl Φ (R n ) = wl p (R n ) is the weak Leesgue space. Next, we recall some lemmas which will e used in our proofs. Lemma.0. Let G, a R n, and r > 0 aritrary. Then χ B(a,r) LΦ (R n ) = where B(a, r) denotes the volume of open all B(a, r). Φ ( ), Let a R n and r > 0. Oserve that χ B(a,r) LΦ (R n ) = inf { > 0: Φ ( ) A = { > 0: Φ ( ) }. Meanwhile, Φ ( ) = inf {r 0: Φ(r) > } = inf A, where } = inf E, where E = {r 0: Φ(r) > }. Choosing = Φ ( ), we have B(a, r) Φ ( ). So we have χ B(a,r) or LΦ (R n ) Φ ( ) < Φ ( ) < r χ B(a,r) LΦ (R n ) Φ ( ). Now, suppose that χ B(a,r) < LΦ (R n ) Φ ( ) χ B(a,r) LΦ (R n ) This contradicts the fact that r. By using the definition of Φ ( ), we can find r E such that. Since r E we otain r A, so we have r χ B(a,r) LΦ (R n ). χ B(a,r) LΦ (R n ). Hence we must have χ B(a,r) = LΦ (R n ) Φ ( ). Furthermore, we have similar result on weak Orlicz space generated y concave function presented in the following Lemma. Lemma..[9]Let G, a R n, and r > 0 is aritrary. Then we have χ B(a,r) = wlφ (R n ) where B(a, r) denotes the volume of open all B(a, r). Φ ( ) 2
4 The 2nd Annual Applied Science and Engineering Conference (AASEC 207) IOP Pulishing IOP Conf. Series: Materials Science and Engineering (208) 0203 doi:0.088/ x/288//0203 Lemma.2. [9] Let G, C <, and 0 t <. Then Φ(Ct) CΦ(t). Lemma.3. Suppose that Φ G and Φ is defined as Φ (t) = inf{ r 0: Φ (r) > t}. Then, the following statements are true: () Φ(Φ (s)) s Φ (Φ(s)), for 0 s <. (2) If, for some constants C, C 2 > 0, we have Φ 2 (s) C Φ (C 2 s), then Φ ( t C ) C 2 Φ 2 (t) fort = Φ 2 (s). We leave the proof of Lemma.3 () to the reader. Now, take aritrary s > 0, and set t = Φ 2 (s). Oserve that y using Lemma.3. (), we have Φ ( t ) = Φ C ( Φ 2 (s) ) Φ (Φ (C 2 s)) C 2 s C By t = Φ 2 (s) and the definition of Φ 2 (s) = inf{ r 0: Φ 2 (r) > s} we gets Φ 2 (t). Hence we can conclude that Φ ( t C ) C 2 Φ 2 (t). 2. Main results In this section, we present two main results which are stated as Theorem 2.. and Theorem 2.2. The following theorem contains a necessary and sufficient condition for the inclusion properties of Orlicz spaces generated y concave function. Theorem 2.. Let Φ, Φ 2 G. Then the following statements are equivalent: () Φ Φ 2. (2) L Φ2 (R n ) L Φ (3) There exist a constant C > 0 such that f LΦ (Rn ) C f LΦ 2 (Rn ), for every f L Φ2 Suppose that () holds. Let f L Φ2 (R n ), then there exist a > 0 such that Hence, we have Φ 2 R n (a f(x) )dx <. Φ ( a R n C f(x) ) dx Φ 2 ( a R n C C f(x) ) dx = Φ 2 (a f(x) )dx <. R n This proves L Φ2 (R n ) L Φ Next, since (L Φ2 (R n ), L Φ (R n )) is a quasi-banach pair, we can prove (2) and (3) are equivalent y similar argument in [3]. Now assume that (3) holds. By Lemma.0., we have Φ ( ) = χ B(a,r) C χ LΦ (Rn ) B(a,r) = LΦ 2 (Rn ) Φ 2 ( C ). In the other words, we have CΦ ( ) Φ 2 ( ) for aritrarya Rn and > 0. By Lemma.3. we have Φ ( t 0 C ) Φ 2(t 0 ) for t 0 = Φ 2 ( ). Since a Rn and > 0 are aritrary, we can conclude that Φ (t) Φ 2 (Ct) fort > 0. 3
5 The 2nd Annual Applied Science and Engineering Conference (AASEC 207) IOP Pulishing IOP Conf. Series: Materials Science and Engineering (208) 0203 doi:0.088/ x/288//0203 We also have otained a necessary and sufficient condition for the inclusion properties of weak Orlicz spaces generated y concave function presented in the following theorem. Theorem 2.2.Let Φ, Φ 2 G. Then the following statements are equivalent: () Φ Φ 2. (2) wl Φ2 (R n ) wl Φ (3) There exist a constant C > 0 such that f wlφ (Rn ) C f wlφ 2 (Rn ), for every f wl Φ2 Suppose that () holds. Let f wl Φ2 (R n ), A Φ = { > 0: sup Φ (t) {x R n : f(x) > t} } and for s = Ct. A Φ2 = { > 0: sup Φ 2 (Ct) {x R n : f(x) > t} } = { > 0: sup Φ 2 (s) {x R n : C f(x) > s} }, Take an aritrary t > 0 and A Φ2, oserve that Φ (t) {x R n : f(x) > t} Φ 2 (Ct) {x R n : f(x) = Φ 2 (s) {x R n : C f(x) > s}. > t} Hence, we have f wlφ (Rn ) = inf A Φ inf A Φ2 = C f wlφ 2 (Rn ), which proves that wl Φ2 (R n ) wl Φ Next, y using similar argument in the Theorem 2.., we can get the equivalence of (2) and (3). Assume that (3) holds. By using Lemma.., we have Φ ( ) = χ B(a,r) C χ wlφ (Rn ) B(a,r) = C wlφ 2 (Rn ) Φ 2 ( ). In the other words, we have CΦ ( ) Φ 2 ( ) for aritrary a Rn and > 0. By Lemma.3., we have Φ ( t 0 C ) Φ 2(t 0 ) for t 0 = Φ 2 ( ). Since a Rn and > 0 are aritrary, we can conclude that Φ (t) Φ 2 (Ct) fort > Concluding remarks We have estalished the sufficient and necessary conditions for inclusion relations among Orlicz spaces and weakorliczspaces generated y concave function. Comining the results on Theorem 2. and Theorem 2.2, we can state that the inclusion relation etween Orlicz spaces generated y concave functions is equivalent to that etween their weak type. Furthermore, it follows from Theorem 2. and Theorem 2.2 that there cannot e an inclusion relation etween L p (R n ) and L p2 (R n )nor wl p (R n ) and wl p2 (R n ) for distinct values of p and p 2. 4
6 The 2nd Annual Applied Science and Engineering Conference (AASEC 207) IOP Pulishing IOP Conf. Series: Materials Science and Engineering (208) 0203 doi:0.088/ x/288//0203 References [] Orlicz W 992 Linear Functional Analysis (Series in Real Analysis Volume 4) World Scientific: Singapore [2] Maligranda L 989 Orlicz Spaces and Interpolation Departamento de Matema tica: Universidade Estadual de Campina [3] Masta A A, Gunawan H and Setya-Budhi W 206 An inclusion property of Orlicz dan weak Orlicz spaces J. Math. Fund. Sci [4] Osançliol A 204 Inclusion etween weighted Orlicz spaces J. Inequal. Appl [5] Masta A A, Gunawan H and Setya-Budhi W 207 An inclusion property of Orlicz-Morrey spaces to appear in J. Phys.: Conf. Ser [6] Masta A A, Gunawan H and Setya-Budhi W 207 An inclusion property of Orlicz-Morrey spaces Research Report ( arxiv: v) [7] Krasnosel skii M A and Rutickii Y A B 96 Convex Functions and Orlicz Spaces, P. Noordhoff LTD.: Groningen [8] Zhou D, Wu L and Jiao Y 207 Martingale weak Orlicz-Karamata-Hardy spaces associated with concave functions J. Math. Anal. Appl [9] Zhang X and Zhang C 20 Weak Orlicz spaces generated y concave functions International Conference on Information Science and Technology (ICIST) [0] Luxemurg W A J 955 Banach Function Spaces Thesis : Technische Hogeschool te Delft 5
Inclusion Properties of Weighted Weak Orlicz Spaces
Inclusion Properties of Weighted Weak Orlicz Spaces Al Azhary Masta, Ifronika 2, Muhammad Taqiyuddin 3,2 Department of Mathematics, Institut Teknologi Bandung Jl. Ganesha no. 0, Bandung arxiv:70.04537v
More informationA Note on Inclusion Properties of Weighted Orlicz Spaces
A Note on Inclusion Properties of Weighted Orlicz Spaces Al Azhary Masta, Ifronika, Muhammad Taqiyuddin 3,3 Department of Mathematics Education, Universitas Pendidikan Indonesia, Jl. Dr. Setiabudi 9, Bandung
More informationSufficient and necessary conditions for generalized Ho lder s inequality in p-summable sequence spaces
Sufficient and necessary conditions for generalized Ho lder s inequality in -suable sequence saces l Masta*, S Fatiah 2, rsisari 3, Y Y Putra 4 and F riani 5,2 Deartent of Matheatics Education, Universitas
More informationCERTAIN PROPERTIES OF GENERALIZED ORLICZ SPACES
Volume 10 (2009), Issue 2, Article 37, 10 pp. CERTAIN PROPERTIES OF GENERALIZED ORLICZ SPACES PANKAJ JAIN AND PRITI UPRETI DEPARTMENT OF MATHEMATICS DESHBANDHU COLLEGE (UNIVERSITY OF DELHI) KALKAJI, NEW
More informationConcentration of magnetic transitions in dilute magnetic materials
Journal of Physics: Conference Series OPEN ACCESS Concentration of magnetic transitions in dilute magnetic materials To cite this article: V I Beloon et al 04 J. Phys.: Conf. Ser. 490 065 Recent citations
More informationNacional de La Pampa, Santa Rosa, La Pampa, Argentina b Instituto de Matemática Aplicada San Luis, Consejo Nacional de Investigaciones Científicas
This article was downloaded by: [Sonia Acinas] On: 28 June 2015, At: 17:05 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer
More informationGeorgian Mathematical Journal 1(94), No. 4, ON THE INITIAL VALUE PROBLEM FOR FUNCTIONAL DIFFERENTIAL SYSTEMS
Georgian Mathematical Journal 1(94), No. 4, 419-427 ON THE INITIAL VALUE PROBLEM FOR FUNCTIONAL DIFFERENTIAL SYSTEMS V. ŠEDA AND J. ELIAŠ Astract. For a system of functional differential equations of an
More informationBoyd Indices of Orlicz Lorentz Spaces
Boyd Indices of Orlicz Lorentz Spaces Department of Mathematics, University of Mis- STEPHEN J MONTGOMERY-SMITH souri, Columbia, Missouri 65211 ABSTRACT Orlicz Lorentz spaces provide a common generalization
More informationInclusion Properties of Orlicz and Weak Orlicz Spaces
J. Math. Fud. Sci., Vol. 48, No. 3, 06, 93-03 93 Iclusio Properties of Orlicz ad Weak Orlicz Spaces Al Azhary Masta,, Hedra Guawa & Woo Setya Budhi Aalysis ad Geometry Group, Faculty of Mathematics ad
More informationFractional integral operators on generalized Morrey spaces of non-homogeneous type 1. I. Sihwaningrum and H. Gunawan
Fractional integral operators on generalized Morrey spaces of non-homogeneous type I. Sihwaningrum and H. Gunawan Abstract We prove here the boundedness of the fractional integral operator I α on generalized
More informationPointwise multipliers on martingale Campanato spaces
arxiv:304.5736v2 [math.pr] Oct 203 Pointwise multipliers on martingale Campanato spaces Eiichi Nakai and Gaku Sadasue Abstract Weintroducegeneralized CampanatospacesL onaprobability space (Ω,F,P), where
More informationOrlicz Lorentz Spaces
Orlicz Lorentz Spaces SJ Montgomery-Smith* Department of Mathematics, University of Missouri, Columbia, MO 65211 It is a great honor to be asked to write this article for the Proceedings of the Conference
More informationPositive Solutions of a Third-Order Three-Point Boundary-Value Problem
Kennesaw State University DigitalCommons@Kennesaw State University Faculty Publications 7-28 Positive Solutions of a Third-Order Three-Point Boundary-Value Problem Bo Yang Kennesaw State University, byang@kennesaw.edu
More informationGENERALIZED STUMMEL CLASS AND MORREY SPACES. Hendra Gunawan, Eiichi Nakai, Yoshihiro Sawano, and Hitoshi Tanaka
PUBLICATIONS DE L INSTITUT MATHÉMATIQUE Nouvelle série, tome 92(6) (22), 27 38 DOI:.2298/PIM2627G GENERALIZED STUMMEL CLASS AND MORREY SPACES Hendra Gunawan, Eiichi Nakai, Yoshihiro Sawano, and Hitoshi
More informationPositive Solutions of Three-Point Nonlinear Second Order Boundary Value Problem
Positive Solutions of Three-Point Nonlinear Second Order Boundary Value Problem YOUSSEF N. RAFFOUL Department of Mathematics University of Dayton, Dayton, OH 45469-236 email:youssef.raffoul@notes.udayton.edu
More informationReaction Wheel Control Design Using Linear Quadratic Controller
IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Reaction Wheel Control Design Using Linear Quadratic Controller To cite this article: Nur Nubli Muhamad et al 2016 IOP Conf. Ser.:
More informationDetermination of Failure Point of Asphalt-Mixture Fatigue-Test Results Using the Flow Number Method
IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Determination of Failure Point of Asphalt-Mixture Fatigue-Test Results Using the Flow Number Method To cite this article: C E
More informationA converse Gaussian Poincare-type inequality for convex functions
Statistics & Proaility Letters 44 999 28 290 www.elsevier.nl/locate/stapro A converse Gaussian Poincare-type inequality for convex functions S.G. Bokov a;, C. Houdre ; ;2 a Department of Mathematics, Syktyvkar
More informationPositive periodic solutions of higher-dimensional nonlinear functional difference equations
J. Math. Anal. Appl. 309 (2005) 284 293 www.elsevier.com/locate/jmaa Positive periodic solutions of higher-dimensional nonlinear functional difference equations Yongkun Li, Linghong Lu Department of Mathematics,
More informationResearch Article The Existence of Countably Many Positive Solutions for Nonlinear nth-order Three-Point Boundary Value Problems
Hindawi Publishing Corporation Boundary Value Problems Volume 9, Article ID 575, 8 pages doi:.55/9/575 Research Article The Existence of Countably Many Positive Solutions for Nonlinear nth-order Three-Point
More informationOn Quadratic Stochastic Operators Having Three Fixed Points
Journal of Physics: Conference Series PAPER OPEN ACCESS On Quadratic Stochastic Operators Having Three Fixed Points To cite this article: Mansoor Saburov and Nur Atikah Yusof 2016 J. Phys.: Conf. Ser.
More informationWEYL-HEISENBERG FRAMES FOR SUBSPACES OF L 2 (R)
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 129, Numer 1, Pages 145 154 S 0002-9939(00)05731-2 Article electronically pulished on July 27, 2000 WEYL-HEISENBERG FRAMES FOR SUBSPACES OF L 2 (R)
More informationDerivation and constants determination of the Freundlich and (fractal) Langmuir adsorption isotherms from kinetics
IOP onference Series: Materials Science and Engineering PAPER OPEN AESS Derivation and constants determination of the Freundlich and (fractal) Langmuir adsorption isotherms from kinetics To cite this article:
More informationRational Chebyshev pseudospectral method for long-short wave equations
Journal of Physics: Conference Series PAPER OPE ACCESS Rational Chebyshev pseudospectral method for long-short wave equations To cite this article: Zeting Liu and Shujuan Lv 07 J. Phys.: Conf. Ser. 84
More informationThe fundamental properties of quasi-semigroups
Journal of Physics: Conference Series PAPER OPEN ACCESS The fundamental properties of quasi-semigroups To cite this article: Sutrima et al 2017 J. Phys.: Conf. Ser. 855 012052 View the article online for
More informationThe Generalized Viscosity Implicit Rules of Asymptotically Nonexpansive Mappings in Hilbert Spaces
Applied Mathematical Sciences, Vol. 11, 2017, no. 12, 549-560 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.718 The Generalized Viscosity Implicit Rules of Asymptotically Nonexpansive
More informationCONVERGENCE OF HYBRID FIXED POINT FOR A PAIR OF NONLINEAR MAPPINGS IN BANACH SPACES
International Journal of Analysis and Applications ISSN 2291-8639 Volume 8, Number 1 2015), 69-78 http://www.etamaths.com CONVERGENCE OF HYBRID FIXED POINT FOR A PAIR OF NONLINEAR MAPPINGS IN BANACH SPACES
More informationHerz (cf. [H], and also [BS]) proved that the reverse inequality is also true, that is,
REARRANGEMENT OF HARDY-LITTLEWOOD MAXIMAL FUNCTIONS IN LORENTZ SPACES. Jesús Bastero*, Mario Milman and Francisco J. Ruiz** Abstract. For the classical Hardy-Littlewood maximal function M f, a well known
More informationPOSITIVE SOLUTIONS FOR BOUNDARY VALUE PROBLEM OF SINGULAR FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATION
International Journal of Pure and Applied Mathematics Volume 92 No. 2 24, 69-79 ISSN: 3-88 (printed version); ISSN: 34-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/.2732/ijpam.v92i2.3
More informationProspective teachers' difficulties in second order linear differential equation: a case of constructing methods in solving a non-homogeneous problem
Journal of Physics: Conference Series PAPER OPEN ACCESS Prospective teachers' difficulties in second order linear differential equation: a case of constructing methods in solving a non-homogeneous problem
More informationMHD free convective flow past a vertical plate
Journal of Physics: Conference Series PAPER OPEN ACCESS MHD free convective flow past a vertical plate To cite this article: Nor Raihan Mohamad Asimoni et al 017 J. Phys.: Conf. Ser. 890 01009 View the
More informationIntroduction to Real Analysis Alternative Chapter 1
Christopher Heil Introduction to Real Analysis Alternative Chapter 1 A Primer on Norms and Banach Spaces Last Updated: March 10, 2018 c 2018 by Christopher Heil Chapter 1 A Primer on Norms and Banach Spaces
More informationRelation between cloud thickness-cloud number concentration differences and rain occurrence based on Koren-Feingold model
Journal of Physics: Conference Series PAPER OPEN ACCESS Relation between cloud thickness-cloud number concentration differences and rain occurrence based on Koren-Feingold model Related content - Recent
More informationIdentification and estimation of state variables on reduced model using balanced truncation method
Journal of Physics: Conference Series PAPER OPEN ACCESS Identification and estimation of state variables on reduced model using balanced truncation method To cite this article: Trifena Punana Lesnussa
More informationOn the split equality common fixed point problem for quasi-nonexpansive multi-valued mappings in Banach spaces
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 (06), 5536 5543 Research Article On the split equality common fixed point problem for quasi-nonexpansive multi-valued mappings in Banach spaces
More informationFUNCTIONAL COMPRESSION-EXPANSION FIXED POINT THEOREM
Electronic Journal of Differential Equations, Vol. 28(28), No. 22, pp. 1 12. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) FUNCTIONAL
More informationProblem Set 2: Solutions Math 201A: Fall 2016
Problem Set 2: s Math 201A: Fall 2016 Problem 1. (a) Prove that a closed subset of a complete metric space is complete. (b) Prove that a closed subset of a compact metric space is compact. (c) Prove that
More informationA NOTE ON LINEAR FUNCTIONAL NORMS
A NOTE ON LINEAR FUNCTIONAL NORMS YIFEI PAN AND MEI WANG Abstract. For a vector u in a normed linear space, Hahn-Banach Theorem provides the existence of a linear functional f, f(u) = u such that f = 1.
More informationThe solution of 4-dimensional Schrodinger equation for Scarf potential and its partner potential constructed By SUSY QM
Journal of Physics: Conference Series PAPER OPEN ACCESS The solution of -dimensional Schrodinger equation for Scarf potential its partner potential constructed By SUSY QM To cite this article: Wahyulianti
More informationEXISTENCE OF POSITIVE SOLUTIONS OF A NONLINEAR SECOND-ORDER BOUNDARY-VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
Electronic Journal of Differential Equations, Vol. 215 (215), No. 236, pp. 1 7. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu EXISTENCE OF POSITIVE
More informationXiyou Cheng Zhitao Zhang. 1. Introduction
Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Center Volume 34, 2009, 267 277 EXISTENCE OF POSITIVE SOLUTIONS TO SYSTEMS OF NONLINEAR INTEGRAL OR DIFFERENTIAL EQUATIONS Xiyou
More informationON ORLICZ-SOBOLEV CAPACITIES
ON ORLICZ-SOBOLEV CAPACITIES JANI JOENSUU Academic dissertation To be presented for public examination with the permission of the Faculty of Science of the University of Helsinki in S12 of the University
More informationNew Iterative Algorithm for Variational Inequality Problem and Fixed Point Problem in Hilbert Spaces
Int. Journal of Math. Analysis, Vol. 8, 2014, no. 20, 995-1003 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4392 New Iterative Algorithm for Variational Inequality Problem and Fixed
More informationHardy spaces with variable exponents and generalized Campanato spaces
Hardy spaces with variable exponents and generalized Campanato spaces Yoshihiro Sawano 1 1 Tokyo Metropolitan University Faculdade de Ciencias da Universidade do Porto Special Session 49 Recent Advances
More informationExistence of Solutions for a Class of p(x)-biharmonic Problems without (A-R) Type Conditions
International Journal of Mathematical Analysis Vol. 2, 208, no., 505-55 HIKARI Ltd, www.m-hikari.com https://doi.org/0.2988/ijma.208.886 Existence of Solutions for a Class of p(x)-biharmonic Problems without
More informationTHE SEMI ORLICZ SPACE cs d 1
Kragujevac Journal of Mathematics Volume 36 Number 2 (2012), Pages 269 276. THE SEMI ORLICZ SPACE cs d 1 N. SUBRAMANIAN 1, B. C. TRIPATHY 2, AND C. MURUGESAN 3 Abstract. Let Γ denote the space of all entire
More informationEXISTENCE RESULTS FOR OPERATOR EQUATIONS INVOLVING DUALITY MAPPINGS VIA THE MOUNTAIN PASS THEOREM
EXISTENCE RESULTS FOR OPERATOR EQUATIONS INVOLVING DUALITY MAPPINGS VIA THE MOUNTAIN PASS THEOREM JENICĂ CRÎNGANU We derive existence results for operator equations having the form J ϕu = N f u, by using
More informationNonlinear elliptic systems with exponential nonlinearities
22-Fez conference on Partial Differential Equations, Electronic Journal of Differential Equations, Conference 9, 22, pp 139 147. http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu
More informationUNIFORMLY CONTINUOUS COMPOSITION OPERATORS IN THE SPACE OF BOUNDED Φ-VARIATION FUNCTIONS IN THE SCHRAMM SENSE
Opuscula Mathematica Vol. 3 No. 01 http://dx.doi.org/10.7494/opmath.01.3..39 UNIFORMLY CONTINUOUS COMPOSITION OPERATORS IN THE SPACE OF BOUNDED Φ-VARIATION FUNCTIONS IN THE SCHRAMM SENSE Tomás Ereú, Nelson
More informationA Note on Nonconvex Minimax Theorem with Separable Homogeneous Polynomials
A Note on Nonconvex Minimax Theorem with Separable Homogeneous Polynomials G. Y. Li Communicated by Harold P. Benson Abstract The minimax theorem for a convex-concave bifunction is a fundamental theorem
More informationReal option valuation for reserve capacity
Real option valuation for reserve capacity MORIARTY, JM; Palczewski, J doi:10.1016/j.ejor.2016.07.003 For additional information aout this pulication click this link. http://qmro.qmul.ac.uk/xmlui/handle/123456789/13838
More informationIndentation tests of aluminium honeycombs
Journal of Physics: Conference Series OPEN ACCESS Indentation tests of aluminium honeycombs To cite this article: A Ashab et al 213 J. Phys.: Conf. Ser. 451 123 View the article online for updates and
More informationDD3MAT - a code for yield criteria anisotropy parameters identification.
Journal of Physics: onference Series PAPER OPEN AESS DD3MA - a code for yield criteria anisotropy parameters identification. o cite this article: P D Barros et al 216 J. Phys.: onf. Ser. 734 3253 View
More informationEXISTENCE OF SOLUTIONS FOR KIRCHHOFF TYPE EQUATIONS WITH UNBOUNDED POTENTIAL. 1. Introduction In this article, we consider the Kirchhoff type problem
Electronic Journal of Differential Equations, Vol. 207 (207), No. 84, pp. 2. ISSN: 072-669. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu EXISTENCE OF SOLUTIONS FOR KIRCHHOFF TYPE EQUATIONS
More informationAnalytic approximation for the modified Bessel function I 2/3
Journal of Physics: Conference Series PAPER OPEN ACCESS Analytic approximation for the modified Bessel function I /3 (x) To cite this article: Pablo Martin et al 017 J. Phys.: Conf. Ser. 936 0100 View
More informationON THE CONVERGENCE OF MODIFIED NOOR ITERATION METHOD FOR NEARLY LIPSCHITZIAN MAPPINGS IN ARBITRARY REAL BANACH SPACES
TJMM 6 (2014), No. 1, 45-51 ON THE CONVERGENCE OF MODIFIED NOOR ITERATION METHOD FOR NEARLY LIPSCHITZIAN MAPPINGS IN ARBITRARY REAL BANACH SPACES ADESANMI ALAO MOGBADEMU Abstract. In this present paper,
More informationWave function regulation to accelarate adiabatic dynamics in quantum mechanics
Journal of Physics: Conference Series PAPER OPEN ACCESS Wave function regulation to accelarate adiabatic dynamics in quantum mechanics To cite this article: Iwan Setiawan et al 2016 J. Phys.: Conf. Ser.
More informationOn Semicontinuity of Convex-valued Multifunctions and Cesari s Property (Q)
On Semicontinuity of Convex-valued Multifunctions and Cesari s Property (Q) Andreas Löhne May 2, 2005 (last update: November 22, 2005) Abstract We investigate two types of semicontinuity for set-valued
More informationNaTa0 3. /MCM-48 composites for photocatalytic conversion of organic molecules. Journal of Physics: Conference Series.
Journal of Physics: Conference Series PAPER OPEN ACCESS NaTa0 3 /MCM-48 composites for photocatalytic conversion of organic molecules To cite this article: K Senevirathne et al 2016 J. Phys.: Conf. Ser.
More informationOn a compactness criteria for multidimensional Hardy type operator in p-convex Banach function spaces
Caspian Journal of Applied Mathematics, Economics and Ecology V. 1, No 1, 2013, July ISSN 1560-4055 On a compactness criteria for multidimensional Hardy type operator in p-convex Banach function spaces
More informationIowa State University. Instructor: Alex Roitershtein Summer Homework #1. Solutions
Math 501 Iowa State University Introduction to Real Analysis Department of Mathematics Instructor: Alex Roitershtein Summer 015 EXERCISES FROM CHAPTER 1 Homework #1 Solutions The following version of the
More informationPositive Periodic Solutions of Systems of Second Order Ordinary Differential Equations
Positivity 1 (26), 285 298 26 Birkhäuser Verlag Basel/Switzerland 1385-1292/2285-14, published online April 26, 26 DOI 1.17/s11117-5-21-2 Positivity Positive Periodic Solutions of Systems of Second Order
More informationNONLINEAR EIGENVALUE PROBLEMS FOR HIGHER ORDER LIDSTONE BOUNDARY VALUE PROBLEMS
NONLINEAR EIGENVALUE PROBLEMS FOR HIGHER ORDER LIDSTONE BOUNDARY VALUE PROBLEMS PAUL W. ELOE Abstract. In this paper, we consider the Lidstone boundary value problem y (2m) (t) = λa(t)f(y(t),..., y (2j)
More informationREARRANGEMENT OF HARDY-LITTLEWOOD MAXIMAL FUNCTIONS IN LORENTZ SPACES
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 128, Number 1, Pages 65 74 S 0002-9939(99)05128-X Article electronically published on June 30, 1999 REARRANGEMENT OF HARDY-LITTLEWOOD MAXIMAL FUNCTIONS
More informationMagnetic properties of soils from landslide potential area (Case study: Pasir Ipis-Lembang, West Bandung)
Journal of Physics: Conference Series PAPER OPEN ACCESS Magnetic properties of soils from landslide potential area (Case study: Pasir Ipis-Lembang, West Bandung) Related content - Magnetic Properties of
More informationStrong convergence of multi-step iterates with errors for generalized asymptotically quasi-nonexpansive mappings
Palestine Journal of Mathematics Vol. 1 01, 50 64 Palestine Polytechnic University-PPU 01 Strong convergence of multi-step iterates with errors for generalized asymptotically quasi-nonexpansive mappings
More informationEstimation of the Minimizer of the Thomas-Fermi- Dirac-von Weizsäcker Functional of NaCl Crystal Lattice
Journal of Physics: Conference Series PAPER OPEN ACCESS Estimation of the Minimizer of the Thomas-Fermi- Dirac-von Weizsäcker Functional of NaCl Crystal Lattice To cite this article: S Wahyuni et al 2016
More informationA WEAK-(p, q) INEQUALITY FOR FRACTIONAL INTEGRAL OPERATOR ON MORREY SPACES OVER METRIC MEASURE SPACES
JMP : Volume 8 Nomor, Juni 206, hal -7 A WEAK-p, q) INEQUALITY FOR FRACTIONAL INTEGRAL OPERATOR ON MORREY SPACES OVER METRIC MEASURE SPACES Idha Sihwaningrum Department of Mathematics, Faculty of Mathematics
More informationStrongly nonlinear parabolic initial-boundary value problems in Orlicz spaces
2002-Fez conference on Partial Differential Equations, Electronic Journal of Differential Equations, Conference 09, 2002, pp 203 220. http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu
More informationA convergence result for an Outer Approximation Scheme
A convergence result for an Outer Approximation Scheme R. S. Burachik Engenharia de Sistemas e Computação, COPPE-UFRJ, CP 68511, Rio de Janeiro, RJ, CEP 21941-972, Brazil regi@cos.ufrj.br J. O. Lopes Departamento
More informationAn Integer Batch Scheduling Model for a Single Machine with Simultaneous Learning and Deterioration Effects to Minimize Total Actual Flow Time
IOP Conference Series: Materials Science and Engineering PAPER OPE ACCESS An Integer Batch Scheduling Model for a Single Machine with Simultaneous Learning and Deterioration Effects to Minimize Total Actual
More informationA Direct Proof of Caristi s Fixed Point Theorem
Applied Mathematical Sciences, Vol. 10, 2016, no. 46, 2289-2294 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.66190 A Direct Proof of Caristi s Fixed Point Theorem Wei-Shih Du Department
More informationComparison of Orlicz Lorentz Spaces
Comparison of Orlicz Lorentz Spaces S.J. Montgomery-Smith* Department of Mathematics, University of Missouri, Columbia, MO 65211. I dedicate this paper to my Mother and Father, who as well as introducing
More informationThe transformation of equation of the characteristic curves to widen the working area of the hall effect sensor
Journal of Physics: Conference Series PAPER OPEN ACCESS The transformation of equation of the characteristic curves to widen the working area of the hall effect sensor To cite this article: D Darmawan
More informationSteepest descent approximations in Banach space 1
General Mathematics Vol. 16, No. 3 (2008), 133 143 Steepest descent approximations in Banach space 1 Arif Rafiq, Ana Maria Acu, Mugur Acu Abstract Let E be a real Banach space and let A : E E be a Lipschitzian
More informationThe Hardy Operator and Boyd Indices
The Hardy Operator and Boyd Indices Department of Mathematics, University of Mis- STEPHEN J MONTGOMERY-SMITH souri, Columbia, Missouri 65211 ABSTRACT We give necessary and sufficient conditions for the
More informationInterpolation via symmetric exponential functions
Journal of Physics: Conference Series OPE ACCESS Interpolation via symmetric exponential functions To cite this article: Agata Bezubik and Severin Pošta 2013 J. Phys.: Conf. Ser. 474 012011 View the article
More informationON THE NONSQUARE CONSTANTS OF L (Φ) [0, + ) Y. Q. YAN
http://dx.doi.org/0.5209/rev_rema.2002.v5.n2.696 ISSN 39-38 ON THE NONSQUARE CONSTANTS OF L (Φ) [0, + ) Y. Q. YAN Abstract Let L (Φ) [0, + ) be the Orlicz function space generated by N function Φ(u) with
More informationFinite element analysis of combined magnetoelectric- electrodynamic vibration energy converter
Journal of Physics: Conference Series PAPER OPEN ACCESS Finite element analysis of combined magnetoelectric- electrodynamic vibration energy converter To cite this article: Sonia Bradai et al 2015 J. Phys.:
More informationSHRINKING PROJECTION METHOD FOR A SEQUENCE OF RELATIVELY QUASI-NONEXPANSIVE MULTIVALUED MAPPINGS AND EQUILIBRIUM PROBLEM IN BANACH SPACES
U.P.B. Sci. Bull., Series A, Vol. 76, Iss. 2, 2014 ISSN 1223-7027 SHRINKING PROJECTION METHOD FOR A SEQUENCE OF RELATIVELY QUASI-NONEXPANSIVE MULTIVALUED MAPPINGS AND EQUILIBRIUM PROBLEM IN BANACH SPACES
More informationOn The Convergence Of Modified Noor Iteration For Nearly Lipschitzian Maps In Real Banach Spaces
CJMS. 2(2)(2013), 95-104 Caspian Journal of Mathematical Sciences (CJMS) University of Mazandaran, Iran http://cjms.journals.umz.ac.ir ISSN: 1735-0611 On The Convergence Of Modified Noor Iteration For
More informationON SUBSPACES OF NON-REFLEXIVE ORLICZ SPACES
ON SUBSPACES OF NON-REFLEXIVE ORLICZ SPACES J. ALEXOPOULOS May 28, 997 ABSTRACT. Kadec and Pelczýnski have shown that every non-reflexive subspace of L (µ) contains a copy of l complemented in L (µ). On
More informationAnalysis of flow characteristics of a cam rotor pump
IOP Conference Series: Materials Science and Engineering OPEN ACCESS Analysis of flow characteristics of a cam rotor pump To cite this article: Y Y Liu et al 2013 IOP Conf. Ser.: Mater. Sci. Eng. 52 032023
More informationSimulation of 1D Gaussian Wave Packet and 2D Waves in Square Membrane Using Excel Spreadsheet with Visual Basic for Teaching Activity
Journal of Physics: Conference Series PAPER OPEN ACCESS Simulation of 1D Gaussian Wave Packet and D Waves in Square Membrane Using Excel Spreadsheet with Visual Basic for Teaching Activity To cite this
More informationIsing Model with Competing Interactions on Cayley Tree of Order 4: An Analytic Solution
Journal of Physics: Conference Series OPEN ACCESS Ising Model with Competing Interactions on Cayley Tree of Order 4: An Analytic Solution To cite this article: Rukiah bin Ali et al 2013 J. Phys.: Conf.
More informationA FIXED POINT THEOREM FOR GENERALIZED NONEXPANSIVE MULTIVALUED MAPPINGS
Fixed Point Theory, (0), No., 4-46 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html A FIXED POINT THEOREM FOR GENERALIZED NONEXPANSIVE MULTIVALUED MAPPINGS A. ABKAR AND M. ESLAMIAN Department of Mathematics,
More informationCommutative Associative Binary Operations on a Set with Five Elements
Journal of Physics: Conference Series PAPER OPEN ACCESS Commutative Associative Binary Operations on a Set with Five Elements To cite this article: Amit Sehgal et al 2018 J. Phys.: Conf. Ser. 1000 012063
More informationAcoustical contribution calculation and analysis of compressor shell based on acoustic transfer vector method
IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Acoustical contribution calculation and analysis of compressor shell based on acoustic transfer vector method o cite this article:
More informationOn nonexpansive and accretive operators in Banach spaces
Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 10 (2017), 3437 3446 Research Article Journal Homepage: www.tjnsa.com - www.isr-publications.com/jnsa On nonexpansive and accretive
More informationA NOTE ON PROJECTION OF FUZZY SETS ON HYPERPLANES
Proyecciones Vol. 20, N o 3, pp. 339-349, December 2001. Universidad Católica del Norte Antofagasta - Chile A NOTE ON PROJECTION OF FUZZY SETS ON HYPERPLANES HERIBERTO ROMAN F. and ARTURO FLORES F. Universidad
More informationOn Super Edge-magic Total Labeling of Modified Watermill Graph
Journal of Physics: Conference Series PAPER OPEN ACCESS On Super Edge-magic Total Labeling of Modified Watermill Graph To cite this article: Nurdin et al 018 J. Phys.: Conf. Ser. 979 01067 View the article
More informationFixed Point Theorems for -Monotone Maps on Partially Ordered S-Metric Spaces
Filomat 28:9 (2014), 1885 1898 DOI 10.2298/FIL1409885D Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Fixed Point Theorems for
More informationSharp estimates of bounded solutions to some semilinear second order dissipative equations
Sharp estimates of ounded solutions to some semilinear second order dissipative equations Cyrine Fitouri & Alain Haraux Astract. Let H, V e two real Hilert spaces such that V H with continuous and dense
More informationSolution existence of variational inequalities with pseudomonotone operators in the sense of Brézis
Solution existence of variational inequalities with pseudomonotone operators in the sense of Brézis B. T. Kien, M.-M. Wong, N. C. Wong and J. C. Yao Communicated by F. Giannessi This research was partially
More informationCapacitary Riesz-Herz and Wiener-Stein estimates
Capacitary Riesz-Herz and Wiener-Stein estimates Joint work with Irina Asekritova and Natan Krugljak J. Cerda, Departament de Matema tica Aplicada i Ana lisi; GARF, Barcelona Riesz-Herz equivalence for
More informationarxiv: v3 [math.ca] 9 Apr 2015
ON THE PRODUCT OF FUNCTIONS IN BMO AND H 1 OVER SPACES OF HOMOGENEOUS TYPE ariv:1407.0280v3 [math.ca] 9 Apr 2015 LUONG DANG KY Abstract. Let be an RD-space, which means that is a space of homogeneous type
More informationNumerical calculation for cavitation flow of inducer
IOP Conference Series: Materials Science and Engineering OPEN ACCESS Numerical calculation for cavitation flow of inducer To cite this article: C Ning et al 2015 IOP Conf. Ser.: Mater. Sci. Eng. 72 032025
More informationOptimization of the blade trailing edge geometric parameters for a small scale ORC turbine
IOP Conference Series: Materials Science and Engineering OPEN ACCESS Optimization of the blade trailing edge geometric parameters for a small scale ORC turbine To cite this article: L Zhang et al 013 IOP
More informationTHROUGHOUT this paper, we let C be a nonempty
Strong Convergence Theorems of Multivalued Nonexpansive Mappings and Maximal Monotone Operators in Banach Spaces Kriengsak Wattanawitoon, Uamporn Witthayarat and Poom Kumam Abstract In this paper, we prove
More informationFree-surface potential flow of an ideal fluid due to a singular sink
Journal of Physics: Conference Series PAPER OPEN ACCESS Free-surface potential flow of an ideal fluid due to a singular sink To cite this article: A A Mestnikova and V N Starovoitov 216 J. Phys.: Conf.
More information