ON SOME NEW INEQUALITIES OF HADAMARD TYPE INVOLVING h-convex FUNCTIONS. 1. Introduction. f(a) + f(b) f(x)dx b a. 2 a
|
|
- Melissa Lynch
- 5 years ago
- Views:
Transcription
1 Act Mth. Univ. Comenine Vol. LXXIX, (00, pp ON SOME NEW INEQUALITIES OF HADAMARD TYPE INVOLVING h-convex FUNCTIONS M. Z. SARIKAYA, E. SET nd M. E. ÖZDEMIR Abstrct. In this pper, we estblish some inequlities o Hdmrd type or h convex unctions.. Introduction Let : I R R be convex mpping deined on the intervl I o rel numbers nd, b I with < b. The ollowing double inequlity (. ( + b ( + (b (xdx b is known in the literture s Hdmrd inequlity or convex mpping. Note tht some o the clssicl inequlities or mens cn be derived rom (. or pproprite prticulr selections o the mpping. Both inequlities hold in the reversed direction i is concve. In [8], Fejér gve generliztion o the inequlity (. s ollows. I : [, b] R is convex unction nd g : [, b] R is nonnegtive, integrble nd symmetric bout +b, then (. ( b + b g(xdx (xg(xdx ( + (b For some results which generlize, improve nd extend the inequlities (. nd (., we reer the reder to the recent ppers (see [6], [7], [], [5]. Deinition ([9]. We sy tht : I R R is Godunov-Levin unction or tht belongs to the clss Q(I i is nonnegtive nd or ll x, y I nd α (0,, we hve (αx + ( αy (x α + (y α. Received Februry 9, 00; revised June 8, Mthemtics Subject Clssiiction. Primry 6D07, 6D5. Key words nd phrses. Hdmrd s inequlity; Convex onction; h-convex unction.
2 66 M. Z. SARIKAYA, E. SET nd M. E. ÖZDEMIR The clss Q(I ws irstly described in [9] by Godunov nd Levin. Some urther properties o it re given in [6], [3] nd [4]. Among the others, it is noted tht nonnegtive monotone nd nonnegtive convex unctions belong to this clss o unctions. Deinition ([]. Let s be rel number, s (0, ]. A unction : [0, [0, is sid to be s-convex (in the second sense or belongs to the clss K s, i or ll x, y [0, nd α [0, ]. (αx + ( αy α s (x + ( α s (y In 978, Breckner introduced s-convex unctions s generliztion o convex unctions []. Also, in the pper Breckner proved the importnt ct tht the set-vlued mp is n s-convex only i the ssocited support unction is s-convex unction [3]. A number o properties nd connections with s-convexity in the irst sense is discussed in pper []. O course, s-convexity mens just convexity when s =. In [] nd [4], Berstein-Doetsch type results were proved on rtionlly s-convex unctions, moreover, or the s-hölder property o s-convex unctions. Deinition 3 ([6]. We sy tht : I R is P -unction or tht belongs to the clss P (I i is nonnegtive nd or ll x, y I nd α [0, ], we hve (αx + ( αy (x + (y. Deinition 4 ([6]. Let h : J R R be nonnegtive unction. We sy tht : I R R is h-convex unction, or belongs to the clss SX(h, I, i is nonnegtive nd or ll x, y I nd α (0,, we hve (.3 (αx + ( αy h(α(x + h( α(y. I inequlity (.3 is reversed, then is sid to be h-concve, i.e. SV (h, I. Obviously, i h(α = α, then ll nonnegtive convex unctions belong to SX(h, I nd ll nonnegtive concve unctions belong to SV (h, I; i h(α = α, then SX(h, I = Q(I; i h(α =, then SX(h, I P (I; nd i h(α = α s, where s (0,, then SX(h, I K s. Proposition ([6]. Let nd g be similrly ordered unctions on I, i.e. ( (x (y (g (x g (y 0 or ll x, y I. I SX (h, I, g SX (h, I nd h(α + h( α c or ll α (0,, where h (t = mx {h (t, h (t} nd c is ixed positive number, then the product g belongs to SX (ch, I. For recent results or h-convex unctions, we reer the reder to the recent ppers (see [], [5], [0], [5]. In [7], Drgomir nd Fitzptrick proved vrint o Hdmrd s inequlity which holds or s-convex unctions in the second sense.
3 HADAMARD TYPE INEQUALITY 67 Theorem ([7]. Suppose tht : [0, [0, is n s-convex unction in the second sense, where s (0,, nd let, b [0,, < b. I L ([, b], then the ollowing inequlities hold (.4 ( + b s (xdx b ( + (b. s + The constnt k = s+ is the best possible in the second inequlity in (.4. In [6], Drgomir et. l. proved two inequlities o Hdmrd type or clsses o Godunov-Levin unctions nd P -unctions. (.5 (.6 Theorem ([6]. Let Q(I,, b I with < b nd L ([, b]. Then ( + b 4 (xdx. b Theorem 3 ([6]. Let P (I,, b I with < b nd L ([, b]. Then ( + b (xdx [( + (b]. b In [5], Sriky et. l. estblished new Hdmrd-type inequlity or h- convex unctions. Theorem 4 ([5]. Let SX(h, I,, b I with < b nd L ([, b]. Then (.7 h( ( + b (xdx [( + (b] b 0 h(αdα. The min purpose o this pper is to estblish new inequlities like those given the in bove theorems, but now or the clss o h-convex unctions.. Min Results In the sequel o the pper, I nd J re intervls on R, (0, J nd unctions h nd re rel nonnegtive unctions deined on J nd I, respectively. Throughout this pper, we suppose tht h( 0. Lemm. Let SX(h, I. Then or ny x in [, b], (. ( + b x (h(α + h( α [( + (b] (x, α [0, ]. I is n h-concve unction, then lso the reversed inequlity holds.
4 68 M. Z. SARIKAYA, E. SET nd M. E. ÖZDEMIR Proo. Any x in [, b] cn be represented s α + ( αb, 0 α. Thus, we obtin ( + b x = ( + b α ( αb = (( α + αb h( α( + h(α(b = (h(α + h( α [( + (b] [h(α( + h( α(b] (h(α + h( α [( + (b] (α + ( αb = (h(α + h( α [( + (b] (x. Theorem 5. Let SX(h, I,, b I with < b, L ([, b] nd g : [, b] R is nonnegtive, integrble nd symmetric bout ( + b /. Then (. (xg(xdx ( + (b ( h ( b x + h b ( x b Proo. Since SX(h, I nd g is nonnegtive, integrble nd symmetric bout ( + b /, we ind tht (xg(xdx = (xg(xdx + ( + b xg( + b xdx = = + h = The proo is complete. ((x + ( + b x g(xdx [ { h ( x b ( + (b ( b x b + x ( x b b + b + b x ] b b g(xdx ( b x b ( + h ( + h ( h ( x (b b ( } b x (b g(xdx b ( b x + h b ( x b Remrk. In Theorem 5, i we choose h(α = α nd g(x =, then (. reduces the second inequlity in (., nd i we tke h(α = α, then (. reduces the second inequlity in (..
5 HADAMARD TYPE INEQUALITY 69 Theorem 6. Let SX(h, I,, b I with < b, L ([, b] nd g : [, b] R is nonnegtive, integrble nd symmetric bout ( + b /. Then (.3 h( ( + b ( + (b b g(xdx (h(α + h( α (xg(xdx Proo. Since SX(h, I nd g : [, b] R is nonnegtive, integrble nd symmetric bout ( + b /, we hve h( ( + b b g(xdx = h( = h( h( = = ( + b g(xdx ( + b x + x g(xdx h( (( + b x + (xg(xdx ( + b xg( + b xdx + (x (xg(xdx This proves the irst inequlity in (.3. On the other hnd, rom Lemm, we hve (xg(xdx = = = ( + b xg( + b xdx + ( + b xg(xdx + (xg(xdx (xg(xdx [(h(α+h( α [(+(b] (x] g(xdx + ( + (b (h(α + h( α (xg(xdx
6 70 M. Z. SARIKAYA, E. SET nd M. E. ÖZDEMIR Remrk. In Theorem 6, i we tke h(α = α, then the inequlity (.3 reduces inequlity to (.. Remrk 3. In Theorem 6, i we tke g(x =, then the inequlity (.3 reduces to the ollowing inequlity h( ( + b ( + (b (xdx (h(α + h( α. b Integrting both sides o the bove inequlity over [0, ] with α, we hve the inequlity (.7. Remrk 4. In Theorem 6, i we tke h(α = α s, s (0, nd g(x =, then the inequlity (.3 reduces to the ollowing inequlity ( + b s ( + (b (xdx (α s + ( α s. b Integrting both sides o the bove inequlity over [0, ] with α, we hve the inequlity (.4. (.4 Theorem 7. Let g SX(ch, I,, b I with < b nd g L ([, b]. Then ( + b ch( (g where c is ixed positive number. b (g(xdx c[(g( + (g(b] Proo. Since g SX(ch, I, α (0,, then 0 h(αdα, (.5 (g (αx + ( α y ch (α (g (x + ch ( α (g (y. For x = t + ( tb, y = ( t + tb nd α = (g( + b ( ch (g (t + ( tb + ch we obtin (g (( t + tb. ( Integrting both sides o the bove inequlity over [0, ], we obtin ( + b (g b ch ( b (g(xdx, which completes the proo o the irst inequlity in (.4.
7 HADAMARD TYPE INEQUALITY 7 The proo o the second inequlity ollows by using (.5 with x = nd y = b nd integrting with respect to α over [0, ]. Tht is, (.6 b (g(xdx c[(g( + (g(b] 0 h(αdα. We obtin inequlities (.4 rom (.5 nd (.6.The proo is complete. Remrk 5. In Theorem 7, i we choose c = nd g(x =, then inequlities o (.4 reduce to inequlities (.7. Reerences. Bombrdelli M. nd Vrošnec S., Properties o h-convex unctions relted to the Hermite- Hdmrd-Fejér inequlities, Comput. Mth. Appl. 58(9 (009, Breckner W. W., Stetigkeitsussgen ür eine Klsse verllgemeinerter konvexer unktionen in topologischen lineren Rumen, Pupl. Inst. Mth. 3 (978, , Continuity o generlized convex nd generlized concve set-vlued unctions, Rev. Anl. Numér. Thkor. Approx. (993, Breckner W. W. nd Orbán G., Continuity properties o rtionlly s -convex mppings with vlues in ordered topologicl liner spce, Bbes-Bolyi University, Kolozsvár, Buri P. nd Házy A., On pproximtely h-convex unctions, Journl o Convex Anlysis 8( (0. 6. Drgomir S. S., Pečrić J. nd Persson L. E., Some inequlities o Hdmrd type, Soochow J. Mth. (995, Drgomir S. S. nd Fitzptrik S., The Hdmrd s inequlity or s-convex unctions in the second sense, Demonstrtion Mth. 3(4, (999, Fejér L., Über die Fourierreihen, II. Mth. Nturwiss, Anz. Ungr. Akd. Wiss., 4 (960, , (In Hungrin. 9. Godunov E. K. nd Levin V. I., Nervenstv dlj unkcii sirokogo klss, soderzscego vypuklye, monotonnye i nekotorye drugie vidy unkii, in: Vycislitel. Mt. i. Fiz. Mezvuzov. Sb. Nuc. Trudov, MGPI, Moskv, 985, Házy A., Bernstein-Doetsch-type results or h-convex unctions, ccepted to Mthemticl Inequlities nd Applictions, (see e.g. pre.pd. Hudzik H. nd Mligrnd L., Some remrks on s-convex unctions, Aequtiones Mth. 48 (994, 00.. Kirmci U. S., Bkul M. K., Ozdemir M. E. nd. Pečrić J., Hdmrd-type inequlities or s-convex unctions, Appl. Mth. nd Compt. 93 (007, Mitrinovic D. S. nd Pečrić J., Note on clss o unctions o Godunov nd Levin, C. R. Mth. Rep. Acd. Sci. Cn. (990, Mitrinovic D. S., Pečrić J. nd Fink A. M., Clssicl nd new inequlities in nlysis, Kluwer Acdemic, Dordrecht, Sriky M. Z., Sglm A. ndyıldırım H., On some Hdmrd type inequlities or h- convex unctions, Jour. Mth. Ineq. (3 (008, Vrošnec S., On h-convexity, J. Mth. Anl. Appl. 36 (007,
8 7 M. Z. SARIKAYA, E. SET nd M. E. ÖZDEMIR M. Z. Sriky, Deprtment o Mthemtics, Fculty o Science nd Arts, Düzce University, Düzce-Turkey, e-mil: srikymz@gmil.com, sriky@ku.edu.tr E. Set, Attürk University, K.K. Eduction Fculty, Deprtment o Mthemtics, 540, Cmpus, Erzurum, Turkey, e-mil: erhnset@yhoo.com M. E. Özdemir, Attürk University, K.K. Eduction Fculty, Deprtment o Mthemtics, 540, Cmpus, Erzurum, Turkey, e-mil: emos@tuni.edu.tr
Hermite-Hadamard type inequalities for harmonically convex functions
Hcettepe Journl o Mthemtics nd Sttistics Volume 43 6 4 935 94 Hermite-Hdmrd type ineulities or hrmoniclly convex unctions İmdt İşcn Abstrct The uthor introduces the concept o hrmoniclly convex unctions
More informationn-points Inequalities of Hermite-Hadamard Type for h-convex Functions on Linear Spaces
Armenin Journl o Mthemtics Volume 8, Number, 6, 38 57 n-points Inequlities o Hermite-Hdmrd Tpe or h-convex Functions on Liner Spces S. S. Drgomir Victori Universit, Universit o the Witwtersrnd Abstrct.
More informationNEW INEQUALITIES OF SIMPSON S TYPE FOR s CONVEX FUNCTIONS WITH APPLICATIONS. := f (4) (x) <. The following inequality. 2 b a
NEW INEQUALITIES OF SIMPSON S TYPE FOR s CONVEX FUNCTIONS WITH APPLICATIONS MOHAMMAD ALOMARI A MASLINA DARUS A AND SEVER S DRAGOMIR B Abstrct In terms of the first derivtive some ineulities of Simpson
More informationOn new Hermite-Hadamard-Fejer type inequalities for p-convex functions via fractional integrals
CMMA, No., -5 7 Communiction in Mthemticl Modeling nd Applictions http://ntmsci.com/cmm On new Hermite-Hdmrd-Fejer type ineulities or p-convex unctions vi rctionl integrls Mehmet Kunt nd Imdt Iscn Deprtment
More informationThe Hadamard s Inequality for s-convex Function
Int. Journl o Mth. Anlysis, Vol., 008, no. 3, 639-646 The Hdmrd s Inequlity or s-conve Function M. Alomri nd M. Drus School o Mthemticl Sciences Fculty o Science nd Technology Universiti Kebngsn Mlysi
More informationOn some refinements of companions of Fejér s inequality via superquadratic functions
Proyecciones Journl o Mthemtics Vol. 3, N o, pp. 39-33, December. Universidd Ctólic del Norte Antogst - Chile On some reinements o compnions o Fejér s inequlity vi superqudrtic unctions Muhmmd Amer Lti
More informationThe Hadamard s inequality for quasi-convex functions via fractional integrals
Annls of the University of Criov, Mthemtics nd Computer Science Series Volume (), 3, Pges 67 73 ISSN: 5-563 The Hdmrd s ineulity for usi-convex functions vi frctionl integrls M E Özdemir nd Çetin Yildiz
More informationBulletin of the. Iranian Mathematical Society
ISSN: 07-060X Print ISSN: 735-855 Online Bulletin of the Irnin Mthemticl Society Vol 3 07, No, pp 09 5 Title: Some extended Simpson-type ineulities nd pplictions Authors: K-C Hsu, S-R Hwng nd K-L Tseng
More informationNew general integral inequalities for quasiconvex functions
NTMSCI 6, No 1, 1-7 18 1 New Trends in Mthemticl Sciences http://dxdoiorg/185/ntmsci1739 New generl integrl ineulities for usiconvex functions Cetin Yildiz Atturk University, K K Eduction Fculty, Deprtment
More informationf (a) + f (b) f (λx + (1 λ)y) max {f (x),f (y)}, x, y [a, b]. (1.1)
TAMKANG JOURNAL OF MATHEMATICS Volume 41, Number 4, 353-359, Winter 1 NEW INEQUALITIES OF HERMITE-HADAMARD TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE QUASI-CONVEX M. ALOMARI, M. DARUS
More informationNew Integral Inequalities of the Type of Hermite-Hadamard Through Quasi Convexity
Punjb University Journl of Mthemtics (ISSN 116-56) Vol. 45 (13) pp. 33-38 New Integrl Inequlities of the Type of Hermite-Hdmrd Through Qusi Convexity S. Hussin Deprtment of Mthemtics, College of Science,
More informationKeywords : Generalized Ostrowski s inequality, generalized midpoint inequality, Taylor s formula.
Generliztions of the Ostrowski s inequlity K. S. Anstsiou Aristides I. Kechriniotis B. A. Kotsos Technologicl Eductionl Institute T.E.I.) of Lmi 3rd Km. O.N.R. Lmi-Athens Lmi 3500 Greece Abstrct Using
More informationOn Hermite-Hadamard type integral inequalities for functions whose second derivative are nonconvex
Mly J Mt 34 93 3 On Hermite-Hdmrd tye integrl ineulities for functions whose second derivtive re nonconvex Mehmet Zeki SARIKAYA, Hkn Bozkurt nd Mehmet Eyü KİRİŞ b Dertment of Mthemtics, Fculty of Science
More informationSome New Inequalities of Simpson s Type for s-convex Functions via Fractional Integrals
Filomt 3:5 (7), 4989 4997 htts://doi.org/.98/fil75989c Published by Fculty o Sciences nd Mthemtics, University o Niš, Serbi Avilble t: htt://www.m.ni.c.rs/ilomt Some New Ineulities o Simson s Tye or s-convex
More informationINEQUALITIES OF HERMITE-HADAMARD TYPE FOR
Preprints (www.preprints.org) NOT PEER-REVIEWED Posted: 7 June 8 doi:.944/preprints86.44.v INEQUALITIES OF HERMITE-HADAMARD TYPE FOR COMPOSITE h-convex FUNCTIONS SILVESTRU SEVER DRAGOMIR ; Abstrct. In
More informationarxiv: v1 [math.ca] 28 Jan 2013
ON NEW APPROACH HADAMARD-TYPE INEQUALITIES FOR s-geometrically CONVEX FUNCTIONS rxiv:3.9v [mth.ca 8 Jn 3 MEVLÜT TUNÇ AND İBRAHİM KARABAYIR Astrct. In this pper we chieve some new Hdmrd type ineulities
More informationOn New Inequalities of Hermite-Hadamard-Fejer Type for Harmonically Quasi-Convex Functions Via Fractional Integrals
X th Interntionl Sttistics Dys Conference ISDC 6), Giresun, Turkey On New Ineulities of Hermite-Hdmrd-Fejer Type for Hrmoniclly Qusi-Convex Functions Vi Frctionl Integrls Mehmet Kunt * nd İmdt İşcn Deprtment
More informationNEW HERMITE HADAMARD INEQUALITIES VIA FRACTIONAL INTEGRALS, WHOSE ABSOLUTE VALUES OF SECOND DERIVATIVES IS P CONVEX
Journl of Mthemticl Ineulities Volume 1, Number 3 18, 655 664 doi:1.7153/jmi-18-1-5 NEW HERMITE HADAMARD INEQUALITIES VIA FRACTIONAL INTEGRALS, WHOSE ABSOLUTE VALUES OF SECOND DERIVATIVES IS P CONVEX SHAHID
More informationOn some inequalities for s-convex functions and applications
Özdemir et l Journl of Ineulities nd Alictions 3, 3:333 htt://wwwjournlofineulitiesndlictionscom/content/3//333 R E S E A R C H Oen Access On some ineulities for s-convex functions nd lictions Muhmet Emin
More informationSome estimates on the Hermite-Hadamard inequality through quasi-convex functions
Annls of University of Criov, Mth. Comp. Sci. Ser. Volume 3, 7, Pges 8 87 ISSN: 13-693 Some estimtes on the Hermite-Hdmrd inequlity through qusi-convex functions Dniel Alexndru Ion Abstrct. In this pper
More informationIntegral inequalities for n times differentiable mappings
JACM 3, No, 36-45 8 36 Journl of Abstrct nd Computtionl Mthemtics http://wwwntmscicom/jcm Integrl ineulities for n times differentible mppings Cetin Yildiz, Sever S Drgomir Attur University, K K Eduction
More informationResearch Article On Hermite-Hadamard Type Inequalities for Functions Whose Second Derivatives Absolute Values Are s-convex
ISRN Applied Mthemtics, Article ID 8958, 4 pges http://dx.doi.org/.55/4/8958 Reserch Article On Hermite-Hdmrd Type Inequlities for Functions Whose Second Derivtives Absolute Vlues Are s-convex Feixing
More informationParametrized inequality of Hermite Hadamard type for functions whose third derivative absolute values are quasi convex
Wu et l. SpringerPlus (5) 4:83 DOI.8/s44-5-33-z RESEARCH Prmetrized inequlity of Hermite Hdmrd type for functions whose third derivtive bsolute vlues re qusi convex Shn He Wu, Bnyt Sroysng, Jin Shn Xie
More informationCo-ordinated s-convex Function in the First Sense with Some Hadamard-Type Inequalities
Int. J. Contemp. Mth. Sienes, Vol. 3, 008, no. 3, 557-567 Co-ordinted s-convex Funtion in the First Sense with Some Hdmrd-Type Inequlities Mohmmd Alomri nd Mslin Drus Shool o Mthemtil Sienes Fulty o Siene
More informationAN INTEGRAL INEQUALITY FOR CONVEX FUNCTIONS AND APPLICATIONS IN NUMERICAL INTEGRATION
Applied Mthemtics E-Notes, 5(005), 53-60 c ISSN 1607-510 Avilble free t mirror sites of http://www.mth.nthu.edu.tw/ men/ AN INTEGRAL INEQUALITY FOR CONVEX FUNCTIONS AND APPLICATIONS IN NUMERICAL INTEGRATION
More informationHadamard-Type Inequalities for s Convex Functions I
Punjb University Journl of Mthemtics ISSN 6-56) Vol. ). 5-6 Hdmrd-Tye Ineulities for s Convex Functions I S. Hussin Dertment of Mthemtics Institute Of Sce Technology, Ner Rwt Toll Plz Islmbd Highwy, Islmbd
More informationINEQUALITIES FOR GENERALIZED WEIGHTED MEAN VALUES OF CONVEX FUNCTION
INEQUALITIES FOR GENERALIZED WEIGHTED MEAN VALUES OF CONVEX FUNCTION BAI-NI GUO AND FENG QI Abstrct. In the rticle, using the Tchebycheff s integrl inequlity, the suitble properties of double integrl nd
More informationAn inequality related to η-convex functions (II)
Int. J. Nonliner Anl. Appl. 6 (15) No., 7-33 ISSN: 8-68 (electronic) http://d.doi.org/1.75/ijn.15.51 An inequlity relted to η-conve functions (II) M. Eshghi Gordji, S. S. Drgomir b, M. Rostmin Delvr, Deprtment
More informationResearch Article Fejér and Hermite-Hadamard Type Inequalities for Harmonically Convex Functions
Hindwi Pulishing Corportion Journl of Applied Mthemtics Volume 4, Article ID 38686, 6 pges http://dx.doi.org/.55/4/38686 Reserch Article Fejér nd Hermite-Hdmrd Type Inequlities for Hrmoniclly Convex Functions
More informationRIEMANN-LIOUVILLE FRACTIONAL SIMPSON S INEQUALITIES THROUGH GENERALIZED (m, h 1, h 2 )-PREINVEXITY
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS N. 38 7 345 37 345 RIEMANN-LIOUVILLE FRACTIONAL SIMPSON S INEQUALITIES THROUGH GENERALIZED m h h -PREINVEXITY Cheng Peng Chng Zhou Tingsong Du Deprtment
More informationGENERALIZATIONS OF WEIGHTED TRAPEZOIDAL INEQUALITY FOR MONOTONIC MAPPINGS AND ITS APPLICATIONS. (b a)3 [f(a) + f(b)] f x (a,b)
GENERALIZATIONS OF WEIGHTED TRAPEZOIDAL INEQUALITY FOR MONOTONIC MAPPINGS AND ITS APPLICATIONS KUEI-LIN TSENG, GOU-SHENG YANG, AND SEVER S. DRAGOMIR Abstrct. In this pper, we estblish some generliztions
More informationOstrowski Grüss Čebyšev type inequalities for functions whose modulus of second derivatives are convex 1
Generl Mthemtics Vol. 6, No. (28), 7 97 Ostrowski Grüss Čebyšev type inequlities for functions whose modulus of second derivtives re convex Nzir Ahmd Mir, Arif Rfiq nd Muhmmd Rizwn Abstrct In this pper,
More informationSome new integral inequalities for n-times differentiable convex and concave functions
Avilble online t wwwisr-ublictionscom/jns J Nonliner Sci Al, 10 017, 6141 6148 Reserch Article Journl Homege: wwwtjnscom - wwwisr-ublictionscom/jns Some new integrl ineulities for n-times differentible
More informationGeneralized Hermite-Hadamard Type Inequalities for p -Quasi- Convex Functions
Ordu Üniv. Bil. Tek. Derg. Cilt:6 Syı: 683-93/Ordu Univ. J. Sci. Tech. Vol:6 No:683-93 -QUASİ-KONVEKS FONKSİYONLAR İÇİN GENELLEŞTİRİLMİŞ HERMİTE-HADAMARD TİPLİ EŞİTSİZLİKLER Özet İm İŞCAN* Giresun Üniversitesi
More informationHermite-Hadamard-Fejér type inequalities for harmonically convex functions via fractional integrals
NTMSCI 4, No. 3, 39-53 6 39 New Trends in Mthemticl Sciences http://d.doi.or/.5/ntmsci.6337 Hermite-Hdmrd-Fejér type ineulities or hrmoniclly conve unctions vi rctionl interls Imdt Iscn, Mehmet Kunt nd
More informationJournal of Inequalities in Pure and Applied Mathematics
Journl of Inequlities in Pure nd Applied Mthemtics GENERALIZATIONS OF THE TRAPEZOID INEQUALITIES BASED ON A NEW MEAN VALUE THEOREM FOR THE REMAINDER IN TAYLOR S FORMULA volume 7, issue 3, rticle 90, 006.
More informationResearch Article On New Inequalities via Riemann-Liouville Fractional Integration
Abstrct nd Applied Anlysis Volume 202, Article ID 428983, 0 pges doi:0.55/202/428983 Reserch Article On New Inequlities vi Riemnn-Liouville Frctionl Integrtion Mehmet Zeki Sriky nd Hsn Ogunmez 2 Deprtment
More informationBounds for the Riemann Stieltjes integral via s-convex integrand or integrator
ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA Volume 6, Number, 0 Avilble online t www.mth.ut.ee/ct/ Bounds for the Riemnn Stieltjes integrl vi s-convex integrnd or integrtor Mohmmd Wjeeh
More informationGeneralized Hermite-Hadamard-Fejer type inequalities for GA-convex functions via Fractional integral
DOI 763/s4956-6-4- Moroccn J Pure nd Appl AnlMJPAA) Volume ), 6, Pges 34 46 ISSN: 35-87 RESEARCH ARTICLE Generlized Hermite-Hdmrd-Fejer type inequlities for GA-conve functions vi Frctionl integrl I mdt
More informationOn the Co-Ordinated Convex Functions
Appl. Mth. In. Si. 8, No. 3, 085-0 0 085 Applied Mthemtis & Inormtion Sienes An Interntionl Journl http://.doi.org/0.785/mis/08038 On the Co-Ordinted Convex Funtions M. Emin Özdemir, Çetin Yıldız, nd Ahmet
More informationHermite-Hadamard Type Inequalities for the Functions whose Second Derivatives in Absolute Value are Convex and Concave
Applied Mthemticl Sciences Vol. 9 05 no. 5-36 HIKARI Ltd www.m-hikri.com http://d.doi.org/0.988/ms.05.9 Hermite-Hdmrd Type Ineulities for the Functions whose Second Derivtives in Absolute Vlue re Conve
More informationInequalities for convex and s-convex functions on Δ =[a, b] [c, d]
Özdemir et l. Journl o Ineulities nd Applitions, : http://www.journloineulitiesndpplitions.om/ontent/// RESEARCH Open Aess Ineulities or onvex nd s-onvex untions on Δ =, b], d] Muhmet Emin Özdemir, Hvv
More informationS. S. Dragomir. 2, we have the inequality. b a
Bull Koren Mth Soc 005 No pp 3 30 SOME COMPANIONS OF OSTROWSKI S INEQUALITY FOR ABSOLUTELY CONTINUOUS FUNCTIONS AND APPLICATIONS S S Drgomir Abstrct Compnions of Ostrowski s integrl ineulity for bsolutely
More informationON A CONVEXITY PROPERTY. 1. Introduction Most general class of convex functions is defined by the inequality
Krgujevc Journl of Mthemtics Volume 40( (016, Pges 166 171. ON A CONVEXITY PROPERTY SLAVKO SIMIĆ Abstrct. In this rticle we proved n interesting property of the clss of continuous convex functions. This
More informationINTEGRAL INEQUALITIES FOR DIFFERENTIABLE RELATIVE HARMONIC PREINVEX FUNCTIONS (SURVEY)
TWMS J. Pure Appl. Mth., V.7, N., 6, pp.3-9 INTEGRAL INEQUALITIES FOR DIFFERENTIABLE RELATIVE HARMONIC PREINVEX FUNCTIONS SURVEY M.A. NOOR, K.I. NOOR, S. IFTIKHAR Abstrct. In this pper, we consider nd
More informationSome Hermite-Hadamard type inequalities for functions whose exponentials are convex
Stud. Univ. Beş-Bolyi Mth. 6005, No. 4, 57 534 Some Hermite-Hdmrd type inequlities for functions whose exponentils re convex Silvestru Sever Drgomir nd In Gomm Astrct. Some inequlities of Hermite-Hdmrd
More informationRevista Colombiana de Matemáticas Volumen 41 (2007), páginas 1 13
Revist Colombin de Mtemátics Volumen 4 7, págins 3 Ostrowski, Grüss, Čebyšev type inequlities for functions whose second derivtives belong to Lp,b nd whose modulus of second derivtives re convex Arif Rfiq
More informationRelative Strongly h-convex Functions and Integral Inequalities
Appl. Mth. Inf. Sci. Lett. 4, No., 39-45 (6) 39 Applied Mthemtics & Informtion Sciences Letters An Interntionl Journl http://dx.doi.org/.8576/misl/4 Reltive Strongly h-convex Functions nd Integrl Inequlities
More informationHadamard-Type Inequalities for s-convex Functions
Interntionl Mthemtil Forum, 3, 008, no. 40, 965-975 Hdmrd-Type Inequlitie or -Convex Funtion Mohmmd Alomri nd Mlin Dru Shool o Mthemtil Siene Fulty o Siene nd Tehnology Univeriti Kebngn Mlyi Bngi 43600
More informationResearch Article On The Hadamard s Inequality for Log-Convex Functions on the Coordinates
Hindwi Publishing Corportion Journl of Inequlities nd Applictions Volume 29, Article ID 28347, 3 pges doi:.55/29/28347 Reserch Article On The Hdmrd s Inequlity for Log-Convex Functions on the Coordintes
More informationON THE WEIGHTED OSTROWSKI INEQUALITY
ON THE WEIGHTED OSTROWSKI INEQUALITY N.S. BARNETT AND S.S. DRAGOMIR School of Computer Science nd Mthemtics Victori University, PO Bo 14428 Melbourne City, VIC 8001, Austrli. EMil: {neil.brnett, sever.drgomir}@vu.edu.u
More informationAndrzej Olbryś. 1. Introduction
t m Mathematical Publications DOI: 10.1515/tmmp-2015-0008 Tatra Mt. Math. Publ. 62 (2015), 105 111 ON SEPARATION BY h-convex FUNCTIONS Andrzej Olbryś ABSTRACT. In the present paper, we establish the necessary
More informationOn the Generalized Weighted Quasi-Arithmetic Integral Mean 1
Int. Journl of Mth. Anlysis, Vol. 7, 2013, no. 41, 2039-2048 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/10.12988/ijm.2013.3499 On the Generlized Weighted Qusi-Arithmetic Integrl Men 1 Hui Sun School
More informationSome inequalities of Hermite-Hadamard type for n times differentiable (ρ, m) geometrically convex functions
Avilble online t www.tjns.com J. Nonliner Sci. Appl. 8 5, 7 Reserch Article Some ineulities of Hermite-Hdmrd type for n times differentible ρ, m geometriclly convex functions Fiz Zfr,, Humir Klsoom, Nwb
More informationJournal of Inequalities in Pure and Applied Mathematics
Journl o Inequlities in Pure nd Applied Mthemtics http://jipm.vu.edu.u/ Volume 6, Issue 4, Article 6, 2005 MROMORPHIC UNCTION THAT SHARS ON SMALL UNCTION WITH ITS DRIVATIV QINCAI ZHAN SCHOOL O INORMATION
More informationA unified generalization of perturbed mid-point and trapezoid inequalities and asymptotic expressions for its error term
An. Ştiinţ. Univ. Al. I. Cuz Işi. Mt. (N.S. Tomul LXIII, 07, f. A unified generliztion of perturbed mid-point nd trpezoid inequlities nd symptotic expressions for its error term Wenjun Liu Received: 7.XI.0
More informationJournal of Inequalities in Pure and Applied Mathematics
Journl of Inequlities in Pure nd Applied Mthemtics http://jipm.vu.edu.u/ Volume 3, Issue, Article 4, 00 ON AN IDENTITY FOR THE CHEBYCHEV FUNCTIONAL AND SOME RAMIFICATIONS P. CERONE SCHOOL OF COMMUNICATIONS
More informationS. S. Dragomir. 1. Introduction. In [1], Guessab and Schmeisser have proved among others, the following companion of Ostrowski s inequality:
FACTA UNIVERSITATIS NIŠ) Ser Mth Inform 9 00) 6 SOME COMPANIONS OF OSTROWSKI S INEQUALITY FOR ABSOLUTELY CONTINUOUS FUNCTIONS AND APPLICATIONS S S Drgomir Dedicted to Prof G Mstroinni for his 65th birthdy
More informationLYAPUNOV-TYPE INEQUALITIES FOR THIRD-ORDER LINEAR DIFFERENTIAL EQUATIONS
Electronic Journl of Differentil Equtions, Vol. 2017 (2017), No. 139, pp. 1 14. ISSN: 1072-6691. URL: http://ejde.mth.txstte.edu or http://ejde.mth.unt.edu LYAPUNOV-TYPE INEQUALITIES FOR THIRD-ORDER LINEAR
More informationGENERALIZED ABSTRACTED MEAN VALUES
GENERALIZED ABSTRACTED MEAN VALUES FENG QI Abstrct. In this rticle, the uthor introduces the generlized bstrcted men vlues which etend the concepts of most mens with two vribles, nd reserches their bsic
More informationTRAPEZOIDAL TYPE INEQUALITIES FOR n TIME DIFFERENTIABLE FUNCTIONS
TRAPEZOIDAL TYPE INEQUALITIES FOR n TIME DIFFERENTIABLE FUNCTIONS S.S. DRAGOMIR AND A. SOFO Abstrct. In this pper by utilising result given by Fink we obtin some new results relting to the trpezoidl inequlity
More informationON THE HERMITE-HADAMARD TYPE INEQUALITIES FOR FRACTIONAL INTEGRAL OPERATOR
Krgujevc ournl of Mthemtics Volume 44(3) (), Pges 369 37. ON THE HERMITE-HADAMARD TYPE INEQUALITIES FOR FRACTIONAL INTEGRAL OPERATOR H. YALDIZ AND M. Z. SARIKAYA Abstrct. In this er, using generl clss
More informationJournal of Inequalities in Pure and Applied Mathematics
Journl of Inequlities in Pure nd Applied Mthemtics http://jipmvueduu/ Volume, Issue, Article, 00 SOME INEQUALITIES FOR THE DISPERSION OF A RANDOM VARIABLE WHOSE PDF IS DEFINED ON A FINITE INTERVAL NS BARNETT,
More informationINEQUALITIES FOR TWO SPECIFIC CLASSES OF FUNCTIONS USING CHEBYSHEV FUNCTIONAL. Mohammad Masjed-Jamei
Fculty of Sciences nd Mthemtics University of Niš Seri Aville t: http://www.pmf.ni.c.rs/filomt Filomt 25:4 20) 53 63 DOI: 0.2298/FIL0453M INEQUALITIES FOR TWO SPECIFIC CLASSES OF FUNCTIONS USING CHEBYSHEV
More informationNew Integral Inequalities for n-time Differentiable Functions with Applications for pdfs
Applied Mthemticl Sciences, Vol. 2, 2008, no. 8, 353-362 New Integrl Inequlities for n-time Differentible Functions with Applictions for pdfs Aristides I. Kechriniotis Technologicl Eductionl Institute
More informationJournal of Inequalities in Pure and Applied Mathematics
Journl of Inequlities in Pure nd Applied Mthemtics ON LANDAU TYPE INEQUALITIES FOR FUNCTIONS WIT ÖLDER CONTINUOUS DERIVATIVES LJ. MARANGUNIĆ AND J. PEČARIĆ Deprtment of Applied Mthemtics Fculty of Electricl
More informationNew Jensen and Hermite Hadamard type inequalities for h-convex interval-valued functions
Zho et l Journl o Inequlities nd Applictions 8 8:3 https://doiorg/86/s366-8-896-3 R E S E A R C H Open Access New Jensen nd Hermite Hdmrd type inequlities or h-convex intervl-vlued unctions Dng Zho,*,
More informationAn optimal 3-point quadrature formula of closed type and error bounds
Revist Colombin de Mtemátics Volumen 8), págins 9- An optiml 3-point qudrture formul of closed type nd error bounds Un fórmul de cudrtur óptim de 3 puntos de tipo cerrdo y error de fronter Nend Ujević,
More informationSOME HARDY TYPE INEQUALITIES WITH WEIGHTED FUNCTIONS VIA OPIAL TYPE INEQUALITIES
SOME HARDY TYPE INEQUALITIES WITH WEIGHTED FUNCTIONS VIA OPIAL TYPE INEQUALITIES R. P. AGARWAL, D. O REGAN 2 AND S. H. SAKER 3 Abstrct. In this pper, we will prove severl new ineulities of Hrdy type with
More informationEÜFBED - Fen Bilimleri Enstitüsü Dergisi Cilt-Sayı: 3-1 Yıl:
EÜFBED - Fen Bilimleri Enstitüsü Dergisi Cilt-Syı: 3- Yıl: 9-9 NEW INEQUALITIES FOR CONVEX FUNCTIONS KONVEKS FONKSİYONLAR İÇİN YENİ EŞİTSİZLİKLER Mevlüt TUNÇ * ve S. Uğur KIRMACI Kilis 7 Arlık Üniversitesi,
More informationMEAN VALUE PROBLEMS OF FLETT TYPE FOR A VOLTERRA OPERATOR
Electronic Journl of Differentil Equtions, Vol. 213 (213, No. 53, pp. 1 7. ISSN: 172-6691. URL: http://ejde.mth.txstte.edu or http://ejde.mth.unt.edu ftp ejde.mth.txstte.edu MEAN VALUE PROBLEMS OF FLETT
More informationAN INEQUALITY OF OSTROWSKI TYPE AND ITS APPLICATIONS FOR SIMPSON S RULE AND SPECIAL MEANS. I. Fedotov and S. S. Dragomir
RGMIA Reserch Report Collection, Vol., No., 999 http://sci.vu.edu.u/ rgmi AN INEQUALITY OF OSTROWSKI TYPE AND ITS APPLICATIONS FOR SIMPSON S RULE AND SPECIAL MEANS I. Fedotov nd S. S. Drgomir Astrct. An
More informationCLASSROOM NOTE Some new mean value theorems of Flett type
Interntionl Journl of Mthemticl Eduction in Science nd Technology 014 http://dxdoiorg/101080/000739x01490457 CLASSROOM NOTE Some new men vlue theorems of Flett type Chenggun Tn nd Songxio Li Deprtment
More informationA Companion of Ostrowski Type Integral Inequality Using a 5-Step Kernel with Some Applications
Filomt 30:3 06, 360 36 DOI 0.9/FIL6360Q Pulished y Fculty of Sciences nd Mthemtics, University of Niš, Seri Aville t: http://www.pmf.ni.c.rs/filomt A Compnion of Ostrowski Type Integrl Inequlity Using
More informationLYAPUNOV-TYPE INEQUALITIES FOR NONLINEAR SYSTEMS INVOLVING THE (p 1, p 2,..., p n )-LAPLACIAN
Electronic Journl of Differentil Equtions, Vol. 203 (203), No. 28, pp. 0. ISSN: 072-669. URL: http://ejde.mth.txstte.edu or http://ejde.mth.unt.edu ftp ejde.mth.txstte.edu LYAPUNOV-TYPE INEQUALITIES FOR
More informationSOME INEQUALITIES FOR THE DISPERSION OF A RANDOM VARIABLE WHOSE PDF IS DEFINED ON A FINITE INTERVAL
SOME INEQUALITIES FOR THE DISPERSION OF A RANDOM VARIABLE WHOSE PDF IS DEFINED ON A FINITE INTERVAL NS BARNETT P CERONE SS DRAGOMIR AND J ROUMELIOTIS Abstrct Some ineulities for the dispersion of rndom
More informationON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX
Journl of Applied Mhemics, Sisics nd Informics JAMSI), 9 ), No. ON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX MEHMET ZEKI SARIKAYA, ERHAN. SET
More informationJournal of Inequalities in Pure and Applied Mathematics
Journl of Inequlities in Pure nd Applied Mthemtics SOME INEQUALITIES FOR THE DISPERSION OF A RANDOM VARI- ABLE WHOSE PDF IS DEFINED ON A FINITE INTERVAL NEIL S. BARNETT, PIETRO CERONE, SEVER S. DRAGOMIR
More informationON COMPANION OF OSTROWSKI INEQUALITY FOR MAPPINGS WHOSE FIRST DERIVATIVES ABSOLUTE VALUE ARE CONVEX WITH APPLICATIONS
Miskolc Mthemticl Notes HU ISSN 787-5 Vol. 3 (), No., pp. 33 8 ON OMPANION OF OSTROWSKI INEQUALITY FOR MAPPINGS WHOSE FIRST DERIVATIVES ABSOLUTE VALUE ARE ONVEX WITH APPLIATIONS MOHAMMAD W. ALOMARI, M.
More informationImprovement of Ostrowski Integral Type Inequalities with Application
Filomt 30:6 06), 56 DOI 098/FIL606Q Published by Fculty of Sciences nd Mthemtics, University of Niš, Serbi Avilble t: http://wwwpmfnicrs/filomt Improvement of Ostrowski Integrl Type Ineulities with Appliction
More informationKRASNOSEL SKII TYPE FIXED POINT THEOREM FOR NONLINEAR EXPANSION
Fixed Point Theory, 13(2012), No. 1, 285-291 http://www.mth.ubbcluj.ro/ nodecj/sfptcj.html KRASNOSEL SKII TYPE FIXED POINT THEOREM FOR NONLINEAR EXPANSION FULI WANG AND FENG WANG School of Mthemtics nd
More informationHermite-Hadamard and Simpson-like Type Inequalities for Differentiable p-quasi-convex Functions
Filomt 3:9 7 5945 5953 htts://doi.org/.98/fil79945i Pulished y Fculty of Sciences nd Mthemtics University of Niš Seri Aville t: htt://www.mf.ni.c.rs/filomt Hermite-Hdmrd nd Simson-like Tye Ineulities for
More informationON CO-ORDINATED OSTROWSKI AND HADAMARD S TYPE INEQUALITIES FOR CONVEX FUNCTIONS II
TJMM 9 (7), No., 35-4 ON CO-ORDINATED OSTROWSKI AND HADAMARD S TYPE INEQUALITIES FOR CONVEX FUNCTIONS II MUHAMMAD MUDDASSAR, NASIR SIDDIQUI, AND MUHAMMAD IQBAL Abstrt. In this rtile, we estblish vrious
More informationGENERALIZED OSTROWSKI TYPE INEQUALITIES FOR FUNCTIONS WHOSE LOCAL FRACTIONAL DERIVATIVES ARE GENERALIZED s-convex IN THE SECOND SENSE
Journl of Alied Mthemtics nd Comuttionl Mechnics 6, 5(4), - wwwmcmczl -ISSN 99-9965 DOI: 75/jmcm64 e-issn 353-588 GENERALIZED OSTROWSKI TYPE INEQUALITIES FOR FUNCTIONS WHOSE LOCAL FRACTIONAL DERIVATIVES
More informationOn The Hermite- Hadamard-Fejér Type Integral Inequality for Convex Function
Turkish Journl o Anlysis nd Numer Theory, 4, Vol., No. 3, 85-89 Aville online h://us.scieu.com/jn//3/6 Science nd Educion Pulishing DOI:.69/jn--3-6 On The Hermie- Hdmrd-Fejér Tye Inegrl Ineuliy or Convex
More informationDIFFERENCE BETWEEN TWO RIEMANN-STIELTJES INTEGRAL MEANS
Krgujev Journl of Mthemtis Volume 38() (204), Pges 35 49. DIFFERENCE BETWEEN TWO RIEMANN-STIELTJES INTEGRAL MEANS MOHAMMAD W. ALOMARI Abstrt. In this pper, severl bouns for the ifferene between two Riemn-
More informationProperties and integral inequalities of Hadamard- Simpson type for the generalized (s, m)-preinvex functions
Avilble online t wwwtjnscom J Nonliner Sci Appl 9 6, 3 36 Reserch Article Properties nd integrl ineulities of Hdmrd- Simpson type for the generlized s, m-preinvex functions Ting-Song Du,b,, Ji-Gen Lio,
More informationNew Hermite-Hadamard and Jensen Type Inequalities for h Convex Functions on Fractal Sets
Revist Colomin de Mtemátics Volumen 56, págins 45-64 New Hermite-Hdmrd nd Jensen Type Inequlities for h Convex Functions on Frctl Sets Nuevs desigulddes del tipo Hermite-Hdmrd y Jensen pr funciones h-convexs
More informationCHEBYSHEV TYPE INEQUALITY ON NABLA DISCRETE FRACTIONAL CALCULUS. 1. Introduction
Frctionl Differentil Clculus Volume 6, Number 2 (216), 275 28 doi:1.7153/fdc-6-18 CHEBYSHEV TYPE INEQUALITY ON NABLA DISCRETE FRACTIONAL CALCULUS SERKAN ASLIYÜCE AND AYŞE FEZA GÜVENILIR (Communicted by
More informationCzechoslovak Mathematical Journal, 55 (130) (2005), , Abbotsford. 1. Introduction
Czechoslovk Mthemticl Journl, 55 (130) (2005), 933 940 ESTIMATES OF THE REMAINDER IN TAYLOR S THEOREM USING THE HENSTOCK-KURZWEIL INTEGRAL, Abbotsford (Received Jnury 22, 2003) Abstrct. When rel-vlued
More informationFRACTIONAL DYNAMIC INEQUALITIES HARMONIZED ON TIME SCALES
FRACTIONAL DYNAMIC INEQUALITIES HARMONIZED ON TIME SCALES M JIBRIL SHAHAB SAHIR Accepted Mnuscript Version This is the unedited version of the rticle s it ppered upon cceptnce by the journl. A finl edited
More informationWENJUN LIU AND QUÔ C ANH NGÔ
AN OSTROWSKI-GRÜSS TYPE INEQUALITY ON TIME SCALES WENJUN LIU AND QUÔ C ANH NGÔ Astrct. In this pper we derive new inequlity of Ostrowski-Grüss type on time scles nd thus unify corresponding continuous
More informationRELATIONS ON BI-PERIODIC JACOBSTHAL SEQUENCE
TJMM 10 018, No., 141-151 RELATIONS ON BI-PERIODIC JACOBSTHAL SEQUENCE S. UYGUN, H. KARATAS, E. AKINCI Abstrct. Following the new generliztion of the Jcobsthl sequence defined by Uygun nd Owusu 10 s ĵ
More informationON AN INTEGRATION-BY-PARTS FORMULA FOR MEASURES
Volume 8 (2007), Issue 4, Article 93, 13 pp. ON AN INTEGRATION-BY-PARTS FORMULA FOR MEASURES A. ČIVLJAK, LJ. DEDIĆ, AND M. MATIĆ AMERICAN COLLEGE OF MANAGEMENT AND TECHNOLOGY ROCHESTER INSTITUTE OF TECHNOLOGY
More informationThe Bochner Integral and the Weak Property (N)
Int. Journl of Mth. Anlysis, Vol. 8, 2014, no. 19, 901-906 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/10.12988/ijm.2014.4367 The Bochner Integrl nd the Wek Property (N) Besnik Bush Memetj University
More informationUNIFORM CONVERGENCE MA 403: REAL ANALYSIS, INSTRUCTOR: B. V. LIMAYE
UNIFORM CONVERGENCE MA 403: REAL ANALYSIS, INSTRUCTOR: B. V. LIMAYE 1. Pointwise Convergence of Sequence Let E be set nd Y be metric spce. Consider functions f n : E Y for n = 1, 2,.... We sy tht the sequence
More informationAsymptotic behavior of intermediate points in certain mean value theorems. III
Stud. Univ. Bbeş-Bolyi Mth. 59(2014), No. 3, 279 288 Asymptotic behvior of intermedite points in certin men vlue theorems. III Tiberiu Trif Abstrct. The pper is devoted to the study of the symptotic behvior
More informationRIEMANN-LIOUVILLE AND CAPUTO FRACTIONAL APPROXIMATION OF CSISZAR S f DIVERGENCE
SARAJEVO JOURNAL OF MATHEMATICS Vol.5 (17 (2009, 3 12 RIEMANN-LIOUVILLE AND CAPUTO FRACTIONAL APPROIMATION OF CSISZAR S f DIVERGENCE GEORGE A. ANASTASSIOU Abstrct. Here re estblished vrious tight probbilistic
More informationMultiple Positive Solutions for the System of Higher Order Two-Point Boundary Value Problems on Time Scales
Electronic Journl of Qulittive Theory of Differentil Equtions 2009, No. 32, -3; http://www.mth.u-szeged.hu/ejqtde/ Multiple Positive Solutions for the System of Higher Order Two-Point Boundry Vlue Problems
More information