Research Article Invariant Statistical Convergence of Sequences of Sets with respect to a Modulus Function
|
|
- Naomi Cobb
- 5 years ago
- Views:
Transcription
1 Hidawi Publishig Corporatio Abstract ad Applied Aalysis, Article ID 88020, 5 pages Research Article Ivariat Statistical Covergece of Sequeces of Sets with respect to a Modulus Fuctio Nimet Pacaroglu ad Fatih Nuray Departmet of Mathematics, Afyo Kocatepe Uiversity, Afyokarahisar, Turkey Correspodece should be addressed to Fatih Nuray; furay@aku.edu.tr Received 5 December 203; Accepted 2 February 204; Published 23 March 204 Academic Editor: Irea Rachůková Copyright 204 N. Pacaroglu ad F. Nuray. This is a ope access article distributed uder the Creative Commos Attributio Licese, which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. We itroduce ad study the cocept of ivariat covergece for sequeces of sets with respect to modulus fuctio f ad give some iclusio relatios.. Itroductio The cocept of statistical covergece for sequeces of real umbers was itroduced by Fast [] adstudiedbyšalát [2] ad others. Let K N ad K ={k :k K}.Thethe atural desity of K is defied by δ(k) = K,ifthe it exists, where K deotes the cardiality of K. Asequecex = (x k ) complex umbers is said to be statistically coverget to L if, for each ε > 0, {k : x k L ε} =0. () Covergece cocept for sequeces of set had bee studied by Beer [3], Aubi ad Frakowska [4], ad Baroti ad Papii [5]. The cocept of statistical covergece of sequeces of set was itroduced by Nuray ad Rhoades [6]i 202.Ulusu ad Nuray [7] itroduced the cocept of Wijsma lacuary statistical covergece of sequeces of set. Similarly, the cocepts of Wijsma ivariat statistical ad Wijsma lacuary ivariat statistical covergece were itroduced by Pacaroglu ad Nuray [8]i 203. Afuctiof : [0, ) [0, ) is called a modulus, if () f(x) = 0 if ad if oly if x=0; (2) f(x+y) f(x)+f(y); (3) f is icreasig; (4) f is cotiuous from the right at 0. A modulus may be ubouded (e.g., f(x) = x p, 0<p< ) or bouded (e.g., f(x)=x/(x+)). Modulus fuctio was itroduced by Nakao [9]i 953. Ruckle [0] usediideaofmodulusfuctiof to costruct a class of FK spaces. Cosider L(f)={x=(x k ): f( x k )<}. (2) The space L(f) is closely related to the space l which is a L(f) space with f(x) = x,forallrealx 0. Maddox [] defied the followig spaces by usig a modulus fuctio f: w 0 (f) = {x s : w(f)={x s: f( x k )=0}, f( x k L )=0for some L},
2 2 Abstract ad Applied Aalysis w (f) = {x s : sup f( x k )<}, where s is space of all complex sequeces. Later, Coor [2] exteded his defiitio by replacig the Cesaro matrix with a arbitrary oegative matrix summability method B=(b k ) as follow: w (B, f) ={x s: 2. Defiitios ad Notatios (3) b,k f( x k L )=0for some L}. Let σ beamappigofthepositiveitegersitoitself.a cotiuous liear fuctioal φ o l, the space of real bouded sequeces, is said to be a ivariat mea or a σ mea, if ad oly if, (4) () φ(x) 0, forallsequecesx=(x ) with x 0for all ; (2) φ(e) =,wheree=(,,,...); (3) φ(x σ() )=φ(x)for all x l. The mappigs φ areassumedtobeoe-to-oesuchthat σ m () = for all positive itegers ad m, whereσ m () deotes the mth iterate of the mappig σ at.thus,φexteds the it fuctioal o c, the space of coverget sequeces, i the sese that φ(x) = x, forallx c.icaseσ is traslatio mappig σ() = +, theσ mea is ofte called a Baach it ad V σ, the set of bouded sequeces all of whose ivariat meas are equal, is the set of almost coverget sequeces. Itcabeshowthat Nuray ad Savaş [3] defied the followig sequece spaces by usig a modulus fuctio f ad a oegative regular matrix B=(b k ): w 0 (B σ,f)={x s: w(b σ,f) ={x s: b k f( x σ k (m) )=0 uiformly i m}, w (B σ,f)={x s:sup,m b k f( x σ k (m) L )=0 for some L, uiformly i m}, b k f( x σ k (m) )<}. Defiitio (see [4]). A set E of positive itegers is said to have uiform ivariat desity of zero if {k : E {σ (m),σ2 (m),...,σ k (m)}} =0 (8) uiformly i m. By usig uiform ivariat desity, the followig defiitio was give. Defiitio 2 (see [0]). A complex umber sequece x=(x k ) is said to be σ-statistically coverget to L if, for every ε>0, {0 k : x σ k (m) L ε} =0 (9) uiformly i m =, 2,.... This will be deoted by S σ x=lor x k L(S σ ). Let (X, ρ) be a metric space. For ay poit x X ad oempty subset A of X, we defie the distace from x to A by (7) d (x, A) = if a A ρ (x, A). (0) V σ = {x=(x ): t m (x) =L uiformly i m, L = σ x}, (5) The cocept of Wijsma covergece was itroduced by Wijsma [7] as follows. Let (X, ρ) be a metric space. For ay oempty closed subsets A, A k X, we say that the sequece {A k } is Wijsma coverget to A if where, k d(x,a k)=d(x, A), () t m (x) = x m +x σ(m) +x σ 2 (m) + +x σ (m). (6) + for each x X. This will be deoted by W A k =A. Covergece cocept for sequeces of set had bee studied by Beer [3], Aubi ad Frakowska [4], ad Baroti ad
3 Abstract ad Applied Aalysis 3 Papii [5]. The cocepts of Wijsma statistical covergece ad Wijsma strog Cesaro summability were itroduced by Nuray ad Rhoades [6] as follows. Let (X, ρ) be a metric space. For ay oempty closed subsets A, A k X,thesequece{A k } is said to be Wijsma strogly Cesaro summable to A if, for each x X, d(x,a k) d(x, A) =0. (2) Let (X, ρ) be a metric space. For ay oempty closed subsets A, A k X,thesequece{A k } is said to be Wijsma statistically coverget to A if, for ε > 0ad each x X, {k : d (x, A k) d(x, A) ε} =0. (3) I this case we write st W A k =Aor A k A(WS). 3. Mai Result The purpose of this paper is, by usig a modulus fuctio, to itroduce ad study ew sequece spaces of sequeces of sets. The followig three defiitios were give i [8]. Defiitio 3. Let (X, ρ) be a metric space. For ay oempty closed subsets A, A k X, we say that the sequece {A k } is Wijsma ivariat coverget to A, if, for each x X, uiformly i m. d (x, A σ k (m)) =d(x, A) (4) I this case, we write A k A(WV σ ) ad the set of all Wijsma ivariat coverget sequeces of sets will be deoted WV σ. Defiitio 4. Let (X, ρ) be a metric space. For ay oempty closed subsets A, A k X, we say that the sequece {A k } is Wijsma strogly ivariat coverget to A, ifforeachx X, d(x,a σ (m)) d(x, A) k =0 (5) uiformly i m. I this case, we write A k A([WV σ ]) adthesetofall Wijsma strogly ivariat coverget sequeces of sets will be deoted [WV σ ]. Defiitio 5. Let (X, ρ) be a metric space. For ay oempty closed subsets A, A k X, we say that the sequece {A k } is Wijsma ivariat statistically coverget to A, if, for each ε>0ad for each x X, {0 k : d(x,a σ k (m) ) d(x, A) ε} =0 (6) uiformly i m. I this case, we write A k A(WS σ ) ad the set of all Wijsma ivariat statistically coverget sequeces of sets will be deoted WS σ. Let (X, ρ) be metric space. For ay oempty closed subsets A, A k Xad x X, we defie the sequeces of sets space [WV σ ] as follows: [WV σ ] ={{A k } sup m, d(x,a σ k (m) ) <}. (7) Now, by usig a modulus fuctio, we itroduce the followig ew sequece spaces of sequeces of sets. Defiitio 6. Let (X, ρ) be a metric space ad f be a modulus fuctio. For ay oempty closed subsets A, A k X,we say that the sequece {A k } is Wijsma strogly ivariat coverget to A with respect to the modulus f, if, for each x X, uiformly i m. f ( d (x, A σ k (m) ) d(x, A) ) =0 (8) I this case we write A k A([WV σ (f)]) ad the set of all Wijsma strogly ivariat coverget sequeces of sets with respect to the modulus f will be deoted [WV σ (f)]. Let (X, ρ) be metric space ad f be a modulus fuctio. For ay oempty closed subsets A, A k Xad x X,we defie the sequeces of sets space [WV σ (f)] as follows: [WV σ (f)] ={{A k }: sup m, f( d(x,a σ k (m) ) )<}. (9) If f(x) = x, the the spaces [WV σ (f)] ad [WV σ (f)] reduce to [WV σ ] ad [WV σ ],respectively. Now we study the relatio betwee WS σ ad [WV σ (f)] covergece. Theorem 7. Let (X, ρ) be a metric space. For ay oempty closed subsets A, A k X.The (i) A k A([WV σ (f)]) implies A k A(WS σ ); (ii) f is bouded ad A k A(WS σ ) implies A k A([WV σ (f)]); (iii) WS σ =[WV σ (f)],iff is bouded. Proof. (i) Let ε>0ad A k A([WV σ (f)]). Theweca write f( d(x,a σ k (m) ) d(x, A) ) f( d(x,a σ k (m) ) d(x, A) ) d(x,a σ k (m) ) d(x,a) ε ε {k : d(x,a σ k (m) ) d(x, A) ε}, which yields the result. (20)
4 4 Abstract ad Applied Aalysis (ii) Suppose that A k A(WS σ ) ad f is bouded, for each m,set G=sup f( k,m d(x,a σ k (m) ) + d (x, A) ). (2) Proof. Let {A k } [WV σ ].Thewecawrite S m = d(x,a σ k (m) ) d(x, A) 0 ( ) (25) Let ε>0ad select N ε such that {k : d(x,a σ k (m) ) d(x, A) ε 2 } < ε 2G, (22) for all m ad > N ε,adsetl(, m, x) = {k : d(x, A σ k (m) ) d(x, A) ε/2}.now,forallm ad >N ε,we have that f( d(x,a σ k (m) ) d(x, A) ) = f( d(x,a σ k (m) ) d(x, A) ) k L(,m,x) < + f( d(x,a σ k (m) ) d(x, A) ) k L(,m,x) ( ε 2G )G+ ( ε 2 )= ε 2 + ε 2 =ε. (23) Hece, {A k } is strogly ivariat coverget to A with respect to the modulus fuctio f. (iii) This is a immediate cosequece of (i) ad (ii). This completes the proof of the theorem. Theorem 8. Let f be a modulus fuctio. The [WV σ (f)] [WV σ (f)]. Proof. Suppose that, {A k } [WV σ (f)].thewecawrite f( d(x,a σ k (m) ) ) = f( d(x,a σ k (m) ) d(x, A) +d(x, A) ) f( d(x,a σ k (m) ) d(x, A) )+ f ( d (x, A) ) f( d(x,a σ k (m) ) d(x, A) )+M f (), (24) where M is a iteger such that d(x, A) < M. Therefore, {A k } [WV σ (f)]. Theorem 9. If f is a modulus fuctio ad {A k } is strogly ivariat coverget to A, the{a k } is strogly ivariat coverget to A with respect to the modulus f;thatis,[wv σ ] [WV σ (f)]. uiformly i m. Let ε>0ad choose δ with 0<δ<such that f(t) < ε for 0 t δ.writea km = d(x,a σ k (m) ) d(x,a), f(a km )=Σ +Σ 2, (26) where the first summatio is over a km δad secod over a km >δ.theσ εad, for a km >δ, f(a km )< a km δ <+[a km ], (27) δ where [z] deotes the iteger part of z. By defiitio modulus fuctio, we have, for a km >δ, f(a km ) (+[ a km δ ]) f () 2f() a km δ. (28) Hece, Σ 2 2f()(a km /δ), which together with Σ ε yields [WV σ ] [WV σ (f)]. Lemma 0 (see [5]). Let f be a modulus fuctio. Let α>0 be give costat. The, there is a costat c > 0 such that f(x)>cx(0<x<α). Theorem. Let {A k } be a bouded sequece ad f be a modulus fuctio. The {A k } is Wijsma strogly ivariat coverget to A with respect to modulus f ifadolyif{a k } is Wijsma strogly ivariat coverget to A;that is, [WV σ (f)] L = [WV σ ], (29) where L deotes the set of bouded sequeces of sets. Proof. TheproofofthetheoremfollowsfromTheorem 9 ad Lemma 0. Coflict of Iterests The authors declare that there is o coflict of iterests regardig the publicatio of this paper. Refereces [] H. Fast, Sur la covergece statistique, Colloquium Mathematicae,vol.2,o.3-4,pp ,95. [2] T. Šalát, O statistically coverget sequeces of real umbers, Mathematica Slovaca,vol.30,o.2,pp.39 50,980. [3] G. Beer, Covergece of cotiuous liear fuctioals ad their level sets, Archiv der Mathematik, vol.52,o.5,pp , 989. [4] J.P.AubiadH.Frakowska,Set Valued Aalysis,Birkhäuser, Bosto, Mass, USA, 990.
5 Abstract ad Applied Aalysis 5 [5] M. Baroti ad P. L. Papii, Covergece of sequeces of sets, i Methods of Fuctioal Aalysis i Approximatio Theory,vol. 76, pp , Birkhäuser, Basel, Switzerlad, 986. [6] F. Nuray ad B. E. Rhoades, Statistical covergece of sequeces of sets, Fasciculi Mathematici, o.49, pp.87 99, 202. [7] U. Ulusu ad F. Nuray, Lacuary statistical covergece sequeces of sets, Progress i Applied Mathematics, vol. 4, o. 2, pp , 202. [8] N. Pacaroglu ad F. Nuray, O ivariat statistically covergece ad lacu-ary ivariat statistically covergece of sequeces of sets, Progress i Applied Mathematics, vol. 5, o. 2, pp , 203. [9] H. Nakao, Cocave modulars, Joural of the Mathematical Society of Japa,vol.5,o.,pp.29 49,953. [0] W. H. Ruckle, FK spaces i which the sequece of coordiate vectors is bouded, Caadia Joural of Mathematics, vol.25, pp , 973. [] I. J. Maddox, Sequece spaces defied by a modulus, Mathematical Proceedigs of the Cambridge Philosophical Society,vol. 00, o., pp. 6 66, 986. [2] J. Coor, O strog matrix summability with respect to a modulus ad statistical covergece, Caadia Mathematical Bulleti, vol. 32, o. 2, pp , 989. [3] F. Nuray ad E. Savaş, Some ew sequece spaces defied by a modulus fuctio, Idia Joural of Pure ad Applied Mathematics,vol.24,o.,pp ,993. [4] E. Savaş, Strogly σ-coverget sequeces, Bulleti of the Calcutta Mathematical Society,vol.8,o.4,pp ,989. [5] E. Savaş, O strog almost A-summability with respect to a modulus ad statistical covergece, Idia Joural of Pure ad Applied Mathematics,vol.23,o.3,pp ,992.
6 Advaces i Operatios Research Hidawi Publishig Corporatio Advaces i Decisio Scieces Hidawi Publishig Corporatio Joural of Applied Mathematics Algebra Hidawi Publishig Corporatio Hidawi Publishig Corporatio Joural of Probability ad Statistics The Scietific World Joural Hidawi Publishig Corporatio Hidawi Publishig Corporatio Iteratioal Joural of Differetial Equatios Hidawi Publishig Corporatio Submit your mauscripts at Iteratioal Joural of Advaces i Combiatorics Hidawi Publishig Corporatio Mathematical Physics Hidawi Publishig Corporatio Joural of Complex Aalysis Hidawi Publishig Corporatio Iteratioal Joural of Mathematics ad Mathematical Scieces Mathematical Problems i Egieerig Joural of Mathematics Hidawi Publishig Corporatio Hidawi Publishig Corporatio Hidawi Publishig Corporatio Discrete Mathematics Joural of Hidawi Publishig Corporatio Discrete Dyamics i Nature ad Society Joural of Fuctio Spaces Hidawi Publishig Corporatio Abstract ad Applied Aalysis Hidawi Publishig Corporatio Hidawi Publishig Corporatio Iteratioal Joural of Joural of Stochastic Aalysis Optimizatio Hidawi Publishig Corporatio Hidawi Publishig Corporatio
Research Article Approximate Riesz Algebra-Valued Derivations
Abstract ad Applied Aalysis Volume 2012, Article ID 240258, 5 pages doi:10.1155/2012/240258 Research Article Approximate Riesz Algebra-Valued Derivatios Faruk Polat Departmet of Mathematics, Faculty of
More informationResearch Article Generalized Vector-Valued Sequence Spaces Defined by Modulus Functions
Hidawi Publishig Corporatio Joural of Iequalities ad Applicatios Volume 00, Article ID 45789, 7 pages doi:0.55/00/45789 Research Article Geeralized Vector-Valued Sequece Spaces Defied by Modulus Fuctios
More informationResearch Article Some E-J Generalized Hausdorff Matrices Not of Type M
Abstract ad Applied Aalysis Volume 2011, Article ID 527360, 5 pages doi:10.1155/2011/527360 Research Article Some E-J Geeralized Hausdorff Matrices Not of Type M T. Selmaogullari, 1 E. Savaş, 2 ad B. E.
More informationSOME SEQUENCE SPACES DEFINED BY ORLICZ FUNCTIONS
ARCHIVU ATHEATICU BRNO Tomus 40 2004, 33 40 SOE SEQUENCE SPACES DEFINED BY ORLICZ FUNCTIONS E. SAVAŞ AND R. SAVAŞ Abstract. I this paper we itroduce a ew cocept of λ-strog covergece with respect to a Orlicz
More informationKorovkin type approximation theorems for weighted αβ-statistical convergence
Bull. Math. Sci. (205) 5:59 69 DOI 0.007/s3373-05-0065-y Korovki type approximatio theorems for weighted αβ-statistical covergece Vata Karakaya Ali Karaisa Received: 3 October 204 / Revised: 3 December
More informationResearch Article A New Second-Order Iteration Method for Solving Nonlinear Equations
Abstract ad Applied Aalysis Volume 2013, Article ID 487062, 4 pages http://dx.doi.org/10.1155/2013/487062 Research Article A New Secod-Order Iteratio Method for Solvig Noliear Equatios Shi Mi Kag, 1 Arif
More informationResearch Article A Note on Ergodicity of Systems with the Asymptotic Average Shadowing Property
Discrete Dyamics i Nature ad Society Volume 2011, Article ID 360583, 6 pages doi:10.1155/2011/360583 Research Article A Note o Ergodicity of Systems with the Asymptotic Average Shadowig Property Risog
More informationSome vector-valued statistical convergent sequence spaces
Malaya J. Mat. 32)205) 6 67 Some vector-valued statistical coverget sequece spaces Kuldip Raj a, ad Suruchi Padoh b a School of Mathematics, Shri Mata Vaisho Devi Uiversity, Katra-82320, J&K, Idia. b School
More informationReview Article Incomplete Bivariate Fibonacci and Lucas p-polynomials
Discrete Dyamics i Nature ad Society Volume 2012, Article ID 840345, 11 pages doi:10.1155/2012/840345 Review Article Icomplete Bivariate Fiboacci ad Lucas p-polyomials Dursu Tasci, 1 Mirac Ceti Firegiz,
More informationResearch Article Korovkin-Type Theorems in Weighted L p -Spaces via Summation Process
Hidawi Publishig Corporatio The Scietific World Joural Volume 203, Article ID 534054, 6 pages http://dx.doi.org/0.55/203/534054 esearch Article Korovi-Type Theorems i Weighted L p -Spaces via Summatio
More informationResearch Article Moment Inequality for ϕ-mixing Sequences and Its Applications
Hidawi Publishig Corporatio Joural of Iequalities ad Applicatios Volume 2009, Article ID 379743, 2 pages doi:0.55/2009/379743 Research Article Momet Iequality for ϕ-mixig Sequeces ad Its Applicatios Wag
More informationResearch Article Convergence Theorems for Finite Family of Multivalued Maps in Uniformly Convex Banach Spaces
Iteratioal Scholarly Research Network ISRN Mathematical Aalysis Volume 2011, Article ID 576108, 13 pages doi:10.5402/2011/576108 Research Article Covergece Theorems for Fiite Family of Multivalued Maps
More informationON STATISTICAL CONVERGENCE AND STATISTICAL MONOTONICITY
Aales Uiv. Sci. Budapest., Sect. Comp. 39 (203) 257 270 ON STATISTICAL CONVERGENCE AND STATISTICAL MONOTONICITY E. Kaya (Mersi, Turkey) M. Kucukasla (Mersi, Turkey) R. Wager (Paderbor, Germay) Dedicated
More informationConvergence of Random SP Iterative Scheme
Applied Mathematical Scieces, Vol. 7, 2013, o. 46, 2283-2293 HIKARI Ltd, www.m-hikari.com Covergece of Radom SP Iterative Scheme 1 Reu Chugh, 2 Satish Narwal ad 3 Vivek Kumar 1,2,3 Departmet of Mathematics,
More informationResearch Article Quasiconvex Semidefinite Minimization Problem
Optimizatio Volume 2013, Article ID 346131, 6 pages http://dx.doi.org/10.1155/2013/346131 Research Article Quasicovex Semidefiite Miimizatio Problem R. Ekhbat 1 ad T. Bayartugs 2 1 Natioal Uiversity of
More informationStatistically Convergent Double Sequence Spaces in 2-Normed Spaces Defined by Orlicz Function
Applied Mathematics, 0,, 398-40 doi:0.436/am.0.4048 Published Olie April 0 (http://www.scirp.org/oural/am) Statistically Coverget Double Sequece Spaces i -Normed Spaces Defied by Orlic Fuctio Abstract
More informationCorrespondence should be addressed to Wing-Sum Cheung,
Hidawi Publishig Corporatio Joural of Iequalities ad Applicatios Volume 2009, Article ID 137301, 7 pages doi:10.1155/2009/137301 Research Article O Pečarić-Raić-Dragomir-Type Iequalities i Normed Liear
More informationResearch Article A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive Differences
Discrete Dyamics i Nature ad Society Article ID 210761 4 pages http://dxdoiorg/101155/2014/210761 Research Article A Uified Weight Formula for Calculatig the Sample Variace from Weighted Successive Differeces
More informationResearch Article The Arens Algebras of Vector-Valued Functions
Fuctio Spaces, Article ID 248925, 4 pages http://dxdoiorg/055/204/248925 Research Article The Ares Algebras of Vector-Valued Fuctios I G Gaiev,2 adoiegamberdiev,2 Departmet of Sciece i Egieerig, Faculty
More informationResearch Article On q-bleimann, Butzer, and Hahn-Type Operators
Abstract ad Applied Aalysis Volume 205, Article ID 480925, 7 pages http://dx.doi.org/0.55/205/480925 Research Article O q-bleima, Butzer, ad Hah-Type Operators Dilek Söylemez Akara Uiversity, Elmadag Vocatioal
More informationStrong Convergence Theorems According. to a New Iterative Scheme with Errors for. Mapping Nonself I-Asymptotically. Quasi-Nonexpansive Types
It. Joural of Math. Aalysis, Vol. 4, 00, o. 5, 37-45 Strog Covergece Theorems Accordig to a New Iterative Scheme with Errors for Mappig Noself I-Asymptotically Quasi-Noexpasive Types Narogrit Puturog Mathematics
More informationNew Results for the Fibonacci Sequence Using Binet s Formula
Iteratioal Mathematical Forum, Vol. 3, 208, o. 6, 29-266 HIKARI Ltd, www.m-hikari.com https://doi.org/0.2988/imf.208.832 New Results for the Fiboacci Sequece Usig Biet s Formula Reza Farhadia Departmet
More informationResearch Article Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems
Abstract ad Applied Aalysis Volume 203, Article ID 39868, 6 pages http://dx.doi.org/0.55/203/39868 Research Article Noexistece of Homocliic Solutios for a Class of Discrete Hamiltoia Systems Xiaopig Wag
More informationReview Article Complete Convergence for Negatively Dependent Sequences of Random Variables
Hidawi Publishig Corporatio Joural of Iequalities ad Applicatios Volume 010, Article ID 50793, 10 pages doi:10.1155/010/50793 Review Article Complete Covergece for Negatively Depedet Sequeces of Radom
More informationWEIGHTED NORLUND-EULER A-STATISTICAL CONVERGENCE FOR SEQUENCES OF POSITIVE LINEAR OPERATORS
Математички Билтен ISSN 035-336X Vol. 38(LXIV) No. 04 (-33) Скопје, Македонија WEIGHTED NORLUND-EULER A-STATISTICAL CONVERGENCE FOR SEQUENCES OF POSITIVE LIAR OPERATORS Elida Hoxha, Erem Aljimi ad Valdete
More informationGeneralized Weighted Statistical Convergence of Double Sequences and Applications
Filomat 30:3 206, 753 762 DOI 02298/FIL603753C Published by Faculty of Scieces ad Mathematics, Uiversity of Niš, Serbia Available at: http://wwwpmfiacrs/filomat Geeralized Weighted Statistical Covergece
More informationOn Weak and Strong Convergence Theorems for a Finite Family of Nonself I-asymptotically Nonexpansive Mappings
Mathematica Moravica Vol. 19-2 2015, 49 64 O Weak ad Strog Covergece Theorems for a Fiite Family of Noself I-asymptotically Noexpasive Mappigs Birol Güdüz ad Sezgi Akbulut Abstract. We prove the weak ad
More informationResearch Article Carleson Measure in Bergman-Orlicz Space of Polydisc
Abstract ad Applied Aalysis Volume 200, Article ID 603968, 7 pages doi:0.55/200/603968 Research Article arleso Measure i Bergma-Orlicz Space of Polydisc A-Jia Xu, 2 ad Zou Yag 3 Departmet of Mathematics,
More informationProperties of Fuzzy Length on Fuzzy Set
Ope Access Library Joural 206, Volume 3, e3068 ISSN Olie: 2333-972 ISSN Prit: 2333-9705 Properties of Fuzzy Legth o Fuzzy Set Jehad R Kider, Jaafar Imra Mousa Departmet of Mathematics ad Computer Applicatios,
More informationUniform Strict Practical Stability Criteria for Impulsive Functional Differential Equations
Global Joural of Sciece Frotier Research Mathematics ad Decisio Scieces Volume 3 Issue Versio 0 Year 03 Type : Double Blid Peer Reviewed Iteratioal Research Joural Publisher: Global Jourals Ic (USA Olie
More informationConvergence of random variables. (telegram style notes) P.J.C. Spreij
Covergece of radom variables (telegram style otes).j.c. Spreij this versio: September 6, 2005 Itroductio As we kow, radom variables are by defiitio measurable fuctios o some uderlyig measurable space
More informationGeneralization of Contraction Principle on G-Metric Spaces
Global Joural of Pure ad Applied Mathematics. ISSN 0973-1768 Volume 14, Number 9 2018), pp. 1159-1165 Research Idia Publicatios http://www.ripublicatio.com Geeralizatio of Cotractio Priciple o G-Metric
More informationResearch Article On the Strong Laws for Weighted Sums of ρ -Mixing Random Variables
Hidawi Publishig Corporatio Joural of Iequalities ad Applicatios Volume 2011, Article ID 157816, 8 pages doi:10.1155/2011/157816 Research Article O the Strog Laws for Weighted Sums of ρ -Mixig Radom Variables
More informationResearch Article Two Expanding Integrable Models of the Geng-Cao Hierarchy
Abstract ad Applied Aalysis Volume 214, Article ID 86935, 7 pages http://d.doi.org/1.1155/214/86935 Research Article Two Epadig Itegrable Models of the Geg-Cao Hierarchy Xiurog Guo, 1 Yufeg Zhag, 2 ad
More informationResearch Article The Rate of Convergence of Lupas q-analogue of the Bernstein Operators
Hidawi Publishig Corporatio Abstract ad Applied Aalysis, Article ID 52709, 6 pages http://dx.doi.org/0.55/204/52709 Research Article The Rate of Covergece of Lupas q-aalogue of the Berstei Operators Hepig
More informationResearch Article Powers of Complex Persymmetric Antitridiagonal Matrices with Constant Antidiagonals
Hidawi Publishig orporatio ISRN omputatioal Mathematics, Article ID 4570, 5 pages http://dx.doi.org/0.55/04/4570 Research Article Powers of omplex Persymmetric Atitridiagoal Matrices with ostat Atidiagoals
More informationGeneralized Weighted Norlund-Euler. Statistical Convergence
It. Joural of Math. Aalysis Vol. 8 24 o. 7 345-354 HIAI td www.m-hiari.com htt//d.doi.org/.2988/ijma.24.42 Geeralized Weighted orlud-uler tatistical Covergece rem A. Aljimi Deartmet of Mathematics Uiversity
More informationWeakly Connected Closed Geodetic Numbers of Graphs
Iteratioal Joural of Mathematical Aalysis Vol 10, 016, o 6, 57-70 HIKARI Ltd, wwwm-hikaricom http://dxdoiorg/101988/ijma01651193 Weakly Coected Closed Geodetic Numbers of Graphs Rachel M Pataga 1, Imelda
More informationA constructive analysis of convex-valued demand correspondence for weakly uniformly rotund and monotonic preference
MPRA Muich Persoal RePEc Archive A costructive aalysis of covex-valued demad correspodece for weakly uiformly rotud ad mootoic preferece Yasuhito Taaka ad Atsuhiro Satoh. May 04 Olie at http://mpra.ub.ui-mueche.de/55889/
More informationSome Common Fixed Point Theorems in Cone Rectangular Metric Space under T Kannan and T Reich Contractive Conditions
ISSN(Olie): 319-8753 ISSN (Prit): 347-671 Iteratioal Joural of Iovative Research i Sciece, Egieerig ad Techology (A ISO 397: 7 Certified Orgaizatio) Some Commo Fixed Poit Theorems i Coe Rectagular Metric
More informationUniversity of Colorado Denver Dept. Math. & Stat. Sciences Applied Analysis Preliminary Exam 13 January 2012, 10:00 am 2:00 pm. Good luck!
Uiversity of Colorado Dever Dept. Math. & Stat. Scieces Applied Aalysis Prelimiary Exam 13 Jauary 01, 10:00 am :00 pm Name: The proctor will let you read the followig coditios before the exam begis, ad
More informationUnique Common Fixed Point Theorem for Three Pairs of Weakly Compatible Mappings Satisfying Generalized Contractive Condition of Integral Type
Iteratioal Refereed Joural of Egieerig ad Sciece (IRJES ISSN (Olie 239-83X (Prit 239-82 Volume 2 Issue 4(April 23 PP.22-28 Uique Commo Fixed Poit Theorem for Three Pairs of Weakly Compatible Mappigs Satisfyig
More informationThe Australian Journal of Mathematical Analysis and Applications
The Australia Joural of Mathematical Aalysis ad Applicatios Volume 6, Issue 1, Article 10, pp. 1-10, 2009 DIFFERENTIABILITY OF DISTANCE FUNCTIONS IN p-normed SPACES M.S. MOSLEHIAN, A. NIKNAM AND S. SHADKAM
More informationCOMPLEX FACTORIZATIONS OF THE GENERALIZED FIBONACCI SEQUENCES {q n } Sang Pyo Jun
Korea J. Math. 23 2015) No. 3 pp. 371 377 http://dx.doi.org/10.11568/kjm.2015.23.3.371 COMPLEX FACTORIZATIONS OF THE GENERALIZED FIBONACCI SEQUENCES {q } Sag Pyo Ju Abstract. I this ote we cosider a geeralized
More informationLecture Notes for Analysis Class
Lecture Notes for Aalysis Class Topological Spaces A topology for a set X is a collectio T of subsets of X such that: (a) X ad the empty set are i T (b) Uios of elemets of T are i T (c) Fiite itersectios
More informationFUNDAMENTALS OF REAL ANALYSIS by
FUNDAMENTALS OF REAL ANALYSIS by Doğa Çömez Backgroud: All of Math 450/1 material. Namely: basic set theory, relatios ad PMI, structure of N, Z, Q ad R, basic properties of (cotiuous ad differetiable)
More informationBest bounds for dispersion of ratio block sequences for certain subsets of integers
Aales Mathematicae et Iformaticae 49 (08 pp. 55 60 doi: 0.33039/ami.08.05.006 http://ami.ui-eszterhazy.hu Best bouds for dispersio of ratio block sequeces for certai subsets of itegers József Bukor Peter
More informationResearch Article Complete Convergence for Maximal Sums of Negatively Associated Random Variables
Hidawi Publishig Corporatio Joural of Probability ad Statistics Volume 010, Article ID 764043, 17 pages doi:10.1155/010/764043 Research Article Complete Covergece for Maximal Sums of Negatively Associated
More informationNew Inequalities of Hermite-Hadamard-like Type for Functions whose Second Derivatives in Absolute Value are Convex
It. Joural of Math. Aalysis, Vol. 8, 1, o. 16, 777-791 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/1.1988/ijma.1.1 New Ieualities of Hermite-Hadamard-like Type for Fuctios whose Secod Derivatives i
More informationMathematica Slovaca. λ-statistical convergence. Mohammad Mursaleen. Terms of use: Persistent URL:
Mathematica Slovaca Mohammad Mursalee λ-statistical covergece Mathematica Slovaca, Vol. 50 (2000), No. 1, 111--115 Persistet URL: http://dml.cz/dmlcz/136769 Terms of use: Mathematical Istitute of the Slovak
More informationDANIELL AND RIEMANN INTEGRABILITY
DANIELL AND RIEMANN INTEGRABILITY ILEANA BUCUR We itroduce the otio of Riema itegrable fuctio with respect to a Daiell itegral ad prove the approximatio theorem of such fuctios by a mootoe sequece of Jorda
More informationInternational Journal of Mathematical Archive-7(6), 2016, Available online through ISSN
Iteratioal Joural of Mathematical Archive-7(6, 06, 04-0 Available olie through www.ijma.ifo ISSN 9 5046 COMMON FIED POINT THEOREM FOR FOUR WEAKLY COMPATIBLE SELFMAPS OF A COMPLETE G METRIC SPACE J. NIRANJAN
More informationResearch Article On the Property N 1
Abstract ad Applied Aalysis Volume 2016, Article ID 1256906, 5 pages http://dx.doi.org/10.1155/2016/1256906 Research Article O the Property N 1 StaisBaw Kowalczyk ad MaBgorzata Turowska Istitute of Mathematics,
More informationCommon Coupled Fixed Point of Mappings Satisfying Rational Inequalities in Ordered Complex Valued Generalized Metric Spaces
IOSR Joural of Mathematics (IOSR-JM) e-issn: 78-578, p-issn:319-765x Volume 10, Issue 3 Ver II (May-Ju 014), PP 69-77 Commo Coupled Fixed Poit of Mappigs Satisfyig Ratioal Iequalities i Ordered Complex
More informationResearch Article On Geodesic Segments in the Infinitesimal Asymptotic Teichmüller Spaces
Joural of Fuctio Spaces Volume 2015, Article ID 276719, 7 pages http://dx.doi.org/10.1155/2015/276719 esearch Article O Geodesic Segmets i the Ifiitesimal Asymptotic Teichmüller Spaces Ya Wu, 1,2 Yi Qi,
More informationResearch Article Nonautonomous Discrete Neuron Model with Multiple Periodic and Eventually Periodic Solutions
Discrete Dyamics i Nature ad Society Volume 21, Article ID 147282, 6 pages http://dx.doi.org/1.11/21/147282 Research Article Noautoomous Discrete Neuro Model with Multiple Periodic ad Evetually Periodic
More informationHÖLDER SUMMABILITY METHOD OF FUZZY NUMBERS AND A TAUBERIAN THEOREM
Iraia Joural of Fuzzy Systems Vol., No. 4, (204 pp. 87-93 87 HÖLDER SUMMABILITY METHOD OF FUZZY NUMBERS AND A TAUBERIAN THEOREM İ. C. ANAK Abstract. I this paper we establish a Tauberia coditio uder which
More informationCouncil for Innovative Research
ABSTRACT ON ABEL CONVERGENT SERIES OF FUNCTIONS ERDAL GÜL AND MEHMET ALBAYRAK Yildiz Techical Uiversity, Departmet of Mathematics, 34210 Eseler, Istabul egul34@gmail.com mehmetalbayrak12@gmail.com I this
More informationSome Results on Certain Symmetric Circulant Matrices
Joural of Iformatics ad Mathematical Scieces Vol 7, No, pp 81 86, 015 ISSN 0975-5748 olie; 0974-875X prit Pulished y RGN Pulicatios http://wwwrgpulicatioscom Some Results o Certai Symmetric Circulat Matrices
More informationREGULARIZATION OF CERTAIN DIVERGENT SERIES OF POLYNOMIALS
REGULARIZATION OF CERTAIN DIVERGENT SERIES OF POLYNOMIALS LIVIU I. NICOLAESCU ABSTRACT. We ivestigate the geeralized covergece ad sums of series of the form P at P (x, where P R[x], a R,, ad T : R[x] R[x]
More informationA Fixed Point Result Using a Function of 5-Variables
Joural of Physical Scieces, Vol., 2007, 57-6 Fixed Poit Result Usig a Fuctio of 5-Variables P. N. Dutta ad Biayak S. Choudhury Departmet of Mathematics Begal Egieerig ad Sciece Uiversity, Shibpur P.O.:
More informationf n (x) f m (x) < ɛ/3 for all x A. By continuity of f n and f m we can find δ > 0 such that d(x, x 0 ) < δ implies that
Lecture 15 We have see that a sequece of cotiuous fuctios which is uiformly coverget produces a limit fuctio which is also cotiuous. We shall stregthe this result ow. Theorem 1 Let f : X R or (C) be a
More informationOn the Variations of Some Well Known Fixed Point Theorem in Metric Spaces
Turkish Joural of Aalysis ad Number Theory, 205, Vol 3, No 2, 70-74 Available olie at http://pubssciepubcom/tjat/3/2/7 Sciece ad Educatio Publishig DOI:0269/tjat-3-2-7 O the Variatios of Some Well Kow
More informationA Study on Total Rebellion Number in Graphs
Joural of Iformatics ad Mathematical Scieces Vol. 9, No. 3, pp. 765 773, 017 ISSN 0975-5748 (olie); 0974-875X (prit) Published by GN Publicatios http://www.rgpublicatios.com Proceedigs of the Coferece
More informationPs(X) E PnSn x (1.2) PS (x) Po=0, and A k,n k > -I we get summablllty A, summabllity (L) and A method of summability respectively.
Iterat. J. Math. & Math. Sci. VOL. 12 NO. (1989) 99106 99 ON (J,p) SUMMABILITY OF FOURIER SERIES S.M. MAZHAR Departmet of Mathematics Kuwait Uiversity P.O. BOX 5969 13060, Safat, Kuwait (Received December
More informationREAL ANALYSIS II: PROBLEM SET 1 - SOLUTIONS
REAL ANALYSIS II: PROBLEM SET 1 - SOLUTIONS 18th Feb, 016 Defiitio (Lipschitz fuctio). A fuctio f : R R is said to be Lipschitz if there exists a positive real umber c such that for ay x, y i the domai
More informationModified Decomposition Method by Adomian and. Rach for Solving Nonlinear Volterra Integro- Differential Equations
Noliear Aalysis ad Differetial Equatios, Vol. 5, 27, o. 4, 57-7 HIKARI Ltd, www.m-hikari.com https://doi.org/.2988/ade.27.62 Modified Decompositio Method by Adomia ad Rach for Solvig Noliear Volterra Itegro-
More informationHAJEK-RENYI-TYPE INEQUALITY FOR SOME NONMONOTONIC FUNCTIONS OF ASSOCIATED RANDOM VARIABLES
HAJEK-RENYI-TYPE INEQUALITY FOR SOME NONMONOTONIC FUNCTIONS OF ASSOCIATED RANDOM VARIABLES ISHA DEWAN AND B. L. S. PRAKASA RAO Received 1 April 005; Revised 6 October 005; Accepted 11 December 005 Let
More informationA) is empty. B) is a finite set. C) can be a countably infinite set. D) can be an uncountable set.
M.A./M.Sc. (Mathematics) Etrace Examiatio 016-17 Max Time: hours Max Marks: 150 Istructios: There are 50 questios. Every questio has four choices of which exactly oe is correct. For correct aswer, 3 marks
More informationCOMMON FIXED POINT THEOREMS VIA w-distance
Bulleti of Mathematical Aalysis ad Applicatios ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 3 Issue 3, Pages 182-189 COMMON FIXED POINT THEOREMS VIA w-distance (COMMUNICATED BY DENNY H. LEUNG) SUSHANTA
More informationON MEAN ERGODIC CONVERGENCE IN THE CALKIN ALGEBRAS
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 00, Number 0, Pages 000 000 S 0002-9939(XX0000-0 ON MEAN ERGODIC CONVERGENCE IN THE CALKIN ALGEBRAS MARCH T. BOEDIHARDJO AND WILLIAM B. JOHNSON 2
More informationIterative Method For Approximating a Common Fixed Point of Infinite Family of Strictly Pseudo Contractive Mappings in Real Hilbert Spaces
Iteratioal Joural of Computatioal ad Applied Mathematics. ISSN 89-4966 Volume 2, Number 2 (207), pp. 293-303 Research Idia Publicatios http://www.ripublicatio.com Iterative Method For Approimatig a Commo
More informationOn the behavior at infinity of an integrable function
O the behavior at ifiity of a itegrable fuctio Emmauel Lesige To cite this versio: Emmauel Lesige. O the behavior at ifiity of a itegrable fuctio. The America Mathematical Mothly, 200, 7 (2), pp.75-8.
More informationBETWEEN QUASICONVEX AND CONVEX SET-VALUED MAPPINGS. 1. Introduction. Throughout the paper we denote by X a linear space and by Y a topological linear
BETWEEN QUASICONVEX AND CONVEX SET-VALUED MAPPINGS Abstract. The aim of this paper is to give sufficiet coditios for a quasicovex setvalued mappig to be covex. I particular, we recover several kow characterizatios
More informationMATH301 Real Analysis (2008 Fall) Tutorial Note #7. k=1 f k (x) converges pointwise to S(x) on E if and
MATH01 Real Aalysis (2008 Fall) Tutorial Note #7 Sequece ad Series of fuctio 1: Poitwise Covergece ad Uiform Covergece Part I: Poitwise Covergece Defiitio of poitwise covergece: A sequece of fuctios f
More informationON SOME TRIGONOMETRIC POWER SUMS
IJMMS 0: 2002 185 191 PII. S016117120200771 http://ijmms.hidawi.com Hidawi Publishig Corp. ON SOME TRIGONOMETRIC POWER SUMS HONGWEI CHEN Received 17 Jue 2001 Usig the geeratig fuctio method, the closed
More informationIt is often useful to approximate complicated functions using simpler ones. We consider the task of approximating a function by a polynomial.
Taylor Polyomials ad Taylor Series It is ofte useful to approximate complicated fuctios usig simpler oes We cosider the task of approximatig a fuctio by a polyomial If f is at least -times differetiable
More informationCitation Journal of Inequalities and Applications, 2012, p. 2012: 90
Title Polar Duals of Covex ad Star Bodies Author(s) Cheug, WS; Zhao, C; Che, LY Citatio Joural of Iequalities ad Applicatios, 2012, p. 2012: 90 Issued Date 2012 URL http://hdl.hadle.et/10722/181667 Rights
More informationINVERSE THEOREMS OF APPROXIMATION THEORY IN L p,α (R + )
Electroic Joural of Mathematical Aalysis ad Applicatios, Vol. 3(2) July 2015, pp. 92-99. ISSN: 2090-729(olie) http://fcag-egypt.com/jourals/ejmaa/ INVERSE THEOREMS OF APPROXIMATION THEORY IN L p,α (R +
More informationChapter 7 Isoperimetric problem
Chapter 7 Isoperimetric problem Recall that the isoperimetric problem (see the itroductio its coectio with ido s proble) is oe of the most classical problem of a shape optimizatio. It ca be formulated
More informationChapter 6 Infinite Series
Chapter 6 Ifiite Series I the previous chapter we cosidered itegrals which were improper i the sese that the iterval of itegratio was ubouded. I this chapter we are goig to discuss a topic which is somewhat
More informationMAT1026 Calculus II Basic Convergence Tests for Series
MAT026 Calculus II Basic Covergece Tests for Series Egi MERMUT 202.03.08 Dokuz Eylül Uiversity Faculty of Sciece Departmet of Mathematics İzmir/TURKEY Cotets Mootoe Covergece Theorem 2 2 Series of Real
More informationDefinition 4.2. (a) A sequence {x n } in a Banach space X is a basis for X if. unique scalars a n (x) such that x = n. a n (x) x n. (4.
4. BASES I BAACH SPACES 39 4. BASES I BAACH SPACES Sice a Baach space X is a vector space, it must possess a Hamel, or vector space, basis, i.e., a subset {x γ } γ Γ whose fiite liear spa is all of X ad
More informationAbsolute Boundedness and Absolute Convergence in Sequence Spaces* Martin Buntinas and Naza Tanović Miller
Absolute Boudedess ad Absolute Covergece i Sequece Spaces* Marti Butias ad Naza Taović Miller 1 Itroductio We maily use stadard otatio as give i sectio 2 For a F K space E, various forms of sectioal boudedess
More informationBounds for the Positive nth-root of Positive Integers
Pure Mathematical Scieces, Vol. 6, 07, o., 47-59 HIKARI Ltd, www.m-hikari.com https://doi.org/0.988/pms.07.7 Bouds for the Positive th-root of Positive Itegers Rachid Marsli Mathematics ad Statistics Departmet
More informationOn a class of convergent sequences defined by integrals 1
Geeral Mathematics Vol. 4, No. 2 (26, 43 54 O a class of coverget sequeces defied by itegrals Dori Adrica ad Mihai Piticari Abstract The mai result shows that if g : [, ] R is a cotiuous fuctio such that
More informationStability of a Monomial Functional Equation on a Restricted Domain
mathematics Article Stability of a Moomial Fuctioal Equatio o a Restricted Domai Yag-Hi Lee Departmet of Mathematics Educatio, Gogju Natioal Uiversity of Educatio, Gogju 32553, Korea; yaghi2@hamail.et
More informationComparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series
Applied Mathematical Scieces, Vol. 7, 03, o. 6, 3-337 HIKARI Ltd, www.m-hikari.com http://d.doi.org/0.988/ams.03.3430 Compariso Study of Series Approimatio ad Covergece betwee Chebyshev ad Legedre Series
More informationCommon Fixed Points for Multivalued Mappings
Advaces i Applied Mathematical Bioscieces. ISSN 48-9983 Volume 5, Number (04), pp. 9-5 Iteratioal Research Publicatio House http://www.irphouse.com Commo Fixed Poits for Multivalued Mappigs Lata Vyas*
More informationAPPROXIMATION BY BERNSTEIN-CHLODOWSKY POLYNOMIALS
Hacettepe Joural of Mathematics ad Statistics Volume 32 (2003), 1 5 APPROXIMATION BY BERNSTEIN-CHLODOWSKY POLYNOMIALS E. İbili Received 27/06/2002 : Accepted 17/03/2003 Abstract The weighted approximatio
More informationThe value of Banach limits on a certain sequence of all rational numbers in the interval (0,1) Bao Qi Feng
The value of Baach limits o a certai sequece of all ratioal umbers i the iterval 0, Bao Qi Feg Departmet of Mathematical Scieces, Ket State Uiversity, Tuscarawas, 330 Uiversity Dr. NE, New Philadelphia,
More informationOn Summability Factors for N, p n k
Advaces i Dyamical Systems ad Applicatios. ISSN 0973-532 Volume Number 2006, pp. 79 89 c Research Idia Publicatios http://www.ripublicatio.com/adsa.htm O Summability Factors for N, p B.E. Rhoades Departmet
More informationSequences and Series of Functions
Chapter 6 Sequeces ad Series of Fuctios 6.1. Covergece of a Sequece of Fuctios Poitwise Covergece. Defiitio 6.1. Let, for each N, fuctio f : A R be defied. If, for each x A, the sequece (f (x)) coverges
More informationResearch Article Approximation by Lupas-Type Operators and Szász-Mirakyan-Type Operators
Hidawi Publishig Corporatio Joural of Applied Mathematics Volume, Article ID 546784, 8 pages doi:.55//546784 Research Article Approximatio by Lupas-Type Operators ad Szász-Mirakya-Type Operators Hee Su
More informationMathematical Methods for Physics and Engineering
Mathematical Methods for Physics ad Egieerig Lecture otes Sergei V. Shabaov Departmet of Mathematics, Uiversity of Florida, Gaiesville, FL 326 USA CHAPTER The theory of covergece. Numerical sequeces..
More informationResearch Article On the Strong Convergence and Complete Convergence for Pairwise NQD Random Variables
Abstract ad Applied Aalysis Volume 204, Article ID 949608, 7 pages http://dx.doi.org/0.55/204/949608 Research Article O the Strog Covergece ad Complete Covergece for Pairwise NQD Radom Variables Aitig
More informationOn equivalent strictly G-convex renormings of Banach spaces
Cet. Eur. J. Math. 8(5) 200 87-877 DOI: 0.2478/s533-00-0050-3 Cetral Europea Joural of Mathematics O equivalet strictly G-covex reormigs of Baach spaces Research Article Nataliia V. Boyko Departmet of
More information} is said to be a Cauchy sequence provided the following condition is true.
Math 4200, Fial Exam Review I. Itroductio to Proofs 1. Prove the Pythagorea theorem. 2. Show that 43 is a irratioal umber. II. Itroductio to Logic 1. Costruct a truth table for the statemet ( p ad ~ r
More informationA NOTE ON SPECTRAL CONTINUITY. In Ho Jeon and In Hyoun Kim
Korea J. Math. 23 (2015), No. 4, pp. 601 605 http://dx.doi.org/10.11568/kjm.2015.23.4.601 A NOTE ON SPECTRAL CONTINUITY I Ho Jeo ad I Hyou Kim Abstract. I the preset ote, provided T L (H ) is biquasitriagular
More informationAdditional Notes on Power Series
Additioal Notes o Power Series Mauela Girotti MATH 37-0 Advaced Calculus of oe variable Cotets Quick recall 2 Abel s Theorem 2 3 Differetiatio ad Itegratio of Power series 4 Quick recall We recall here
More information