ON THE OSTROWSKI-GRÜSS TYPE INEQUALITY FOR TWICE DIFFERENTIABLE FUNCTIONS

Size: px
Start display at page:

Download "ON THE OSTROWSKI-GRÜSS TYPE INEQUALITY FOR TWICE DIFFERENTIABLE FUNCTIONS"

Transcription

1 Hceepe Journl of Mhemics nd Sisics Volume 45) 0), ON THE OSTROWSKI-GRÜSS TYPE INEQUALITY FOR TWICE DIFFERENTIABLE FUNCTIONS M Emin Özdemir, Ahme Ock Akdemir nd Erhn Se Received 6:06:0 : Acceped 0:0:0 Absrc In his pper we obin some new Osrowski-Grüss ype inequliies conining wice differenible funcions Keywords: Osrowski-Grüss Inequliy 000 AMS Clssificion: Primry: 6D5, 6A07 Inroducion In [], Osrowski proved he following inequliy Theorem Le f : I R, where I R is n inervl, be mpping differenible in he inerior of I nd,b I o, < b If f M, [,b], hen we hve ) f) [ ) f)d +b ] 4 + )M, ) for [,b] In he ps severl yers here hs been considerble ineres in he sudy of Osrowski ype inequliies In [], Özdemir e l proved Osrowski s ype inequliies for α,m)- conve funcions nd in [5], n Osrowski ype inequliy ws given by Srıky However, some new ypes of inequliy re esblished, for emple inequliies of Osrowski- Grüss ype nd inequliies of Osrowski-Chebyshev ype In[9], Milovnović nd Pečrić gve generlizion of Osrowski s inequliy nd some reled pplicions Aurk Universiy, KK Educion Fculy, Deprmen of Mhemics, 5640, Kmpus, Erzurum, Turkey E-mil: emos@uniedur Ağrı İbrhim Çeçen Universiy, Fculy of Science nd Ars, Deprmen of Mhemics, 0400, Ağrı, Turkey E-mil: hmekdemir@griedur Duzce Universiy, Fculy of Science nd Ars, Deprmen of Mhemics, Düzce, Turkey E-mil: erhnse@yhoocom Corresponding Auhor

2 65 ME Özdemir, AO Akdemir, E Se An Osrowski-Grüss ype inequliy ws given for he firs ime by Drgomir nd Wng in [4] In [8], Mić e l, generlized nd improved his inequliy For generlizions, improvemens nd recen resuls see he ppers [] [0], [], [4], [6] nd [8] Recenly, in [7], Ujević proved following heorems; Theorem Le f : I R, where I R is n inervl, be mpping differenible in he inerior of I nd,b I o, < b If here eis consns γ,γ R such h γ f ) Γ, [,b] nd f L [,b], hen we hve ) nd ) f) +b ) fb)f) f) +b ) fb)f) where S = fb)f) f) d ) S γ) f) d ) ΓS), Theorem Le f : I R, where I R is n inervl, be wice coninuously differenible mpping in he inerior of I wih f L [,b] nd,b I o, < b Then we hve 4) f) for [,b] +b ) fb)f) f) d ) π f, The min purpose of his pper is o prove Osrowski-Grüss ype inequliies similr o bove bu now involving wice differenible mppings Min Resuls Theorem Le f : I R, where I R is n inervl, be wice differenible mpping in he inerior of I nd,b I o, < b If here eis consns γ,γ R such h γ f ) Γ, [,b] nd f L [,b], hen we hve f)f ) f )b f b) ) ) ) +b+b f b)f ) f) d nd ) ) S γ) f)f ) f )b f b) ) ) +b+b f b)f ) where S = f b)f ) ) ΓS) f) d

3 Inequliy for Twice Differenible Funcions 65 Proof We cn define mpping K,) s follows: K,) = { ), [,], b),,b] By using his mpping nd inegring by prs, we hve ) K,)f )d = By simple compuion, we hve 4) nd 5) b )f )d+ = f )f)+ f )b f b) ) K,)d = +b+b f )d = f b)f ) Using ), 4) nd 5), we ge We se b)f )d + f )f)+ f )b f b) ) ) +b+b f b)f ) + = R n) = K,)f )d K,)f )d ) ) f )d f )d f) d f) d K,)d K,)d If we wrie R n) s follows wih C R n rbirry consn, hen we hve 6) R n) = f )C ) K,) K,s)ds d We know h 7) K,) K,s)ds d = 0

4 654 ME Özdemir, AO Akdemir, E Se So, if we choose C = γ in 6) Then we ge R n) = f )γ ) K,) nd 8) R n) m [,b] K,) Since nd +b+b ) m K,) +b+b = ) [,b] f )γ d = f b)f )γ) K,s)ds d ) b f )γ d from 8) we hve = S γ)), 9) R n) ) which gives ) S γ), Secondly, if we choose C = Γ in 6) hen by similr rgumen we ge 0) R n) m [,b] K,) nd ) +b+b f )Γ d = Γ)f b)+f ) = ΓS)) so from 0) nd ), we ge ) ) b f )Γ d Theorem Le f : I R, where I R is n inervl, be wice coninuously differenible mpping in he inerior of I wih f L [,b] nd,b I o, < b Then we hve f)f ) f )b f b) ) ) ) +b+b f b)f ) f) d ) where S = f b)f ) )) +b S f,

5 Inequliy for Twice Differenible Funcions 655 Proof Le R n) be defined s in he equliy 6) wih C R n rbirry consn If we choose C = f ) +b, we ge R n) m [,b] K,) +b+b By simple compuion, we ge he required resul References ) b ) +b f )f d [] Ansssiou, GA Osrowski ype inequliies, Proc Amer Mh Soc, , 995 [] Cerone, P, Drgomir, S S Roumeliois, J An inequliy of Osrowski-Grüss ype for wice differenible mppings nd pplicions in numericl inegrion, KYUNGPOOK Mh J 9), 4, 999 [] Cheng, X L Improvemen of some Osrowski-Grüss ype inequliies, Compuers & Mhemics wih Applicions 4/), 09 4, 00 [4] Drgomir, S S nd Wng, S An inequliy of Osrowski-Grüss ype nd is pplicions o he esimion of error bounds for some specil mens nd for some numericl qudrure rules, Compuers & Mhemics wih Applicions ), 5 0, 997 [5] Feng, Q nd Meng, F Some generlized Osrowski Grüss ype inegrl inequliies, Compuers & Mhemics wih Applicions 6), , 0 [6] Liu, Z Some Osrowski Grüss ype inequliies nd pplicions, Compuers & Mhemics wih Applicions 5, 7 79, 007 [7] Liu, Z A shrp generlized Osrowski-Grüss inequliy, Tmsui Oford Journl of Mhemicl Sciences 4), 75 84, 008 [8] Mić, M, Pečrić, J nd Ujević, N Improvemen nd furher generlizion of some inequliies of Osrowski-Grüss ype, Compuers & Mhemics wih Applicions 9/4), 6 75, 000 [9] Milovnović, G V nd Pečrić, J E On generlizion of he inequliy of A Osrowski nd some reled pplicions, Univ Beogrd Publ Elekroehn Fk Ser M Fiz ), 55 58, 976 [0] Niezgod, M A new inequliy of Osrowski Grüss ype nd pplicions o some numericl qudrure rules, Compuers & Mhemics wih Applicions 58), , 009 [] Osrowski, A Über die Absolubweichung einer differenierbren Funkion von ihren Inegrlmielwer, Commen Mh Helv 0, 6 7, 98 [] Özdemir, M E, Kvurmcı, H nd Se, E Osrowski s ype inequliies for α, m)-conve funcions, KYUNGPOOK Mh J 50, 7 78, 00 [] Pchpe, BG On Čebyšev-Grüss ype inequliies vi Pečrić s eension of he Mongomery ideniy, J Inequl Pure Appl Mh 7), Aricle, 006 [4] Perce, C E M, Pečrić, J, Ujević, N nd Vroš, S Generlizions of some inequliies of Osrowski Grüss ype, Mh Inequl Appl ), 5 4, 000 [5] Srıky, M Z On he Osrowski ype inegrl inequliy, Ac Mh Univ Comeninee LXXIX), 9 4, 00 [6] Tong, F nd Gun, L A simple proof of he generlized Osrowski-Grüss ype inegrl inequliy, In Journl of Mh Anlysis 8), , 008 [7] Ujević, N New bounds for he firs inequliy of Osrowski-Grüss ype nd pplicions, Compuers & Mhemics wih Applicions 46, 4 47, 00 [8] Yng, S A unified pproch o some inequliies of Osrowski Grüss ype, Compuers & Mhemics wih Applicions 5, , 006

ON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX

ON 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 information

Hermite-Hadamard-Fejér type inequalities for convex functions via fractional integrals

Hermite-Hadamard-Fejér type inequalities for convex functions via fractional integrals Sud. Univ. Beş-Bolyi Mh. 6(5, No. 3, 355 366 Hermie-Hdmrd-Fejér ype inequliies for convex funcions vi frcionl inegrls İmd İşcn Asrc. In his pper, firsly we hve eslished Hermie Hdmrd-Fejér inequliy for

More information

ON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX.

ON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX. ON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX. MEHMET ZEKI SARIKAYA?, ERHAN. SET, AND M. EMIN OZDEMIR Asrc. In his noe, we oin new some ineuliies

More information

FURTHER GENERALIZATIONS. QI Feng. The value of the integral of f(x) over [a; b] can be estimated in a variety ofways. b a. 2(M m)

FURTHER GENERALIZATIONS. QI Feng. The value of the integral of f(x) over [a; b] can be estimated in a variety ofways. b a. 2(M m) Univ. Beogrd. Pul. Elekroehn. Fk. Ser. M. 8 (997), 79{83 FUTHE GENEALIZATIONS OF INEQUALITIES FO AN INTEGAL QI Feng Using he Tylor's formul we prove wo inegrl inequliies, h generlize K. S. K. Iyengr's

More information

1. Introduction. 1 b b

1. Introduction. 1 b b Journl of Mhemicl Inequliies Volume, Number 3 (007), 45 436 SOME IMPROVEMENTS OF GRÜSS TYPE INEQUALITY N. ELEZOVIĆ, LJ. MARANGUNIĆ AND J. PEČARIĆ (communiced b A. Čižmešij) Absrc. In his pper some inequliies

More information

GENERALIZATION OF SOME INEQUALITIES VIA RIEMANN-LIOUVILLE FRACTIONAL CALCULUS

GENERALIZATION OF SOME INEQUALITIES VIA RIEMANN-LIOUVILLE FRACTIONAL CALCULUS - TAMKANG JOURNAL OF MATHEMATICS Volume 5, Number, 7-5, June doi:5556/jkjm555 Avilble online hp://journlsmhkueduw/ - - - GENERALIZATION OF SOME INEQUALITIES VIA RIEMANN-LIOUVILLE FRACTIONAL CALCULUS MARCELA

More information

Research Article New General Integral Inequalities for Lipschitzian Functions via Hadamard Fractional Integrals

Research Article New General Integral Inequalities for Lipschitzian Functions via Hadamard Fractional Integrals Hindwi Pulishing orporion Inernionl Journl of Anlysis, Aricle ID 35394, 8 pges hp://d.doi.org/0.55/04/35394 Reserch Aricle New Generl Inegrl Inequliies for Lipschizin Funcions vi Hdmrd Frcionl Inegrls

More information

Research Article Generalized Fractional Integral Inequalities for Continuous Random Variables

Research Article Generalized Fractional Integral Inequalities for Continuous Random Variables Journl of Proiliy nd Sisics Volume 2015, Aricle ID 958980, 7 pges hp://dx.doi.org/10.1155/2015/958980 Reserch Aricle Generlized Frcionl Inegrl Inequliies for Coninuous Rndom Vriles Adullh Akkur, Zeynep

More information

On The Hermite- Hadamard-Fejér Type Integral Inequality for Convex Function

On 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 information

EÜFBED - Fen Bilimleri Enstitüsü Dergisi Cilt-Sayı: 3-2 Yıl:

EÜFBED - Fen Bilimleri Enstitüsü Dergisi Cilt-Sayı: 3-2 Yıl: 63 EÜFBED - Fen Bilimleri Ensiüsü Dergisi Cil-Syı: 3- Yıl: 63-7 SOME INEQUALITIES OF HERMITE-HADAMARD TYPE FOR FUNCTIONS WHOSE DERIVATIVES ABSOLUTE VALUES ARE QUASI-CONVEX TÜREVİNİN MUTLAK DEĞERİ QUASI-KONVEKS

More information

Contraction Mapping Principle Approach to Differential Equations

Contraction Mapping Principle Approach to Differential Equations epl Journl of Science echnology 0 (009) 49-53 Conrcion pping Principle pproch o Differenil Equions Bishnu P. Dhungn Deprmen of hemics, hendr Rn Cmpus ribhuvn Universiy, Khmu epl bsrc Using n eension of

More information

Convergence of Singular Integral Operators in Weighted Lebesgue Spaces

Convergence of Singular Integral Operators in Weighted Lebesgue Spaces EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 10, No. 2, 2017, 335-347 ISSN 1307-5543 www.ejpm.com Published by New York Business Globl Convergence of Singulr Inegrl Operors in Weighed Lebesgue

More information

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A SECOND-ORDER ITERATIVE BOUNDARY-VALUE PROBLEM

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A SECOND-ORDER ITERATIVE BOUNDARY-VALUE PROBLEM Elecronic Journl of Differenil Equions, Vol. 208 (208), No. 50, pp. 6. ISSN: 072-669. URL: hp://ejde.mh.xse.edu or hp://ejde.mh.un.edu EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A SECOND-ORDER ITERATIVE

More information

Hermite-Hadamard and Simpson Type Inequalities for Differentiable Quasi-Geometrically Convex Functions

Hermite-Hadamard and Simpson Type Inequalities for Differentiable Quasi-Geometrically Convex Functions Trkish Jornl o Anlysis nd Nmer Theory, 4, Vol, No, 4-46 Aville online h://ssciecom/jn/// Science nd Edcion Plishing DOI:69/jn--- Hermie-Hdmrd nd Simson Tye Ineliies or Dierenile Qsi-Geomericlly Convex

More information

Improvement of Ostrowski Integral Type Inequalities with Application

Improvement 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 information

2k 1. . And when n is odd number, ) The conclusion is when n is even number, an. ( 1) ( 2 1) ( k 0,1,2 L )

2k 1. . And when n is odd number, ) The conclusion is when n is even number, an. ( 1) ( 2 1) ( k 0,1,2 L ) Scholrs Journl of Engineering d Technology SJET) Sch. J. Eng. Tech., ; A):8-6 Scholrs Acdemic d Scienific Publisher An Inernionl Publisher for Acdemic d Scienific Resources) www.sspublisher.com ISSN -X

More information

New Inequalities in Fractional Integrals

New Inequalities in Fractional Integrals ISSN 1749-3889 (prin), 1749-3897 (online) Inernionl Journl of Nonliner Science Vol.9(21) No.4,pp.493-497 New Inequliies in Frcionl Inegrls Zoubir Dhmni Zoubir DAHMANI Lborory of Pure nd Applied Mhemics,

More information

A unified generalization of perturbed mid-point and trapezoid inequalities and asymptotic expressions for its error term

A 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 information

On the Co-Ordinated Convex Functions

On 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 information

AN INTEGRAL INEQUALITY FOR CONVEX FUNCTIONS AND APPLICATIONS IN NUMERICAL INTEGRATION

AN 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 information

Solutions for Nonlinear Partial Differential Equations By Tan-Cot Method

Solutions for Nonlinear Partial Differential Equations By Tan-Cot Method IOSR Journl of Mhemics (IOSR-JM) e-issn: 78-578. Volume 5, Issue 3 (Jn. - Feb. 13), PP 6-11 Soluions for Nonliner Pril Differenil Equions By Tn-Co Mehod Mhmood Jwd Abdul Rsool Abu Al-Sheer Al -Rfidin Universiy

More information

On Hadamard and Fejér-Hadamard inequalities for Caputo k-fractional derivatives

On Hadamard and Fejér-Hadamard inequalities for Caputo k-fractional derivatives In J Nonliner Anl Appl 9 8 No, 69-8 ISSN: 8-68 elecronic hp://dxdoiorg/75/ijn8745 On Hdmrd nd Fejér-Hdmrd inequliies for Cpuo -frcionl derivives Ghulm Frid, Anum Jved Deprmen of Mhemics, COMSATS Universiy

More information

Application on Inner Product Space with. Fixed Point Theorem in Probabilistic

Application on Inner Product Space with. Fixed Point Theorem in Probabilistic Journl of Applied Mhemics & Bioinformics, vol.2, no.2, 2012, 1-10 ISSN: 1792-6602 prin, 1792-6939 online Scienpress Ld, 2012 Applicion on Inner Produc Spce wih Fixed Poin Theorem in Probbilisic Rjesh Shrivsv

More information

A Generalized Inequality of Ostrowski Type for Twice Differentiable Bounded Mappings and Applications

A Generalized Inequality of Ostrowski Type for Twice Differentiable Bounded Mappings and Applications Applied Mthemticl Sciences, Vol. 8, 04, no. 38, 889-90 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.988/ms.04.4 A Generlized Inequlity of Ostrowski Type for Twice Differentile Bounded Mppings nd Applictions

More information

CALDERON S REPRODUCING FORMULA FOR DUNKL CONVOLUTION

CALDERON S REPRODUCING FORMULA FOR DUNKL CONVOLUTION Avilble online hp://scik.org Eng. Mh. Le. 15, 15:4 ISSN: 49-9337 CALDERON S REPRODUCING FORMULA FOR DUNKL CONVOLUTION PANDEY, C. P. 1, RAKESH MOHAN AND BHAIRAW NATH TRIPATHI 3 1 Deprmen o Mhemics, Ajy

More information

Positive and negative solutions of a boundary value problem for a

Positive and negative solutions of a boundary value problem for a Invenion Journl of Reerch Technology in Engineering & Mngemen (IJRTEM) ISSN: 2455-3689 www.ijrem.com Volume 2 Iue 9 ǁ Sepemer 28 ǁ PP 73-83 Poiive nd negive oluion of oundry vlue prolem for frcionl, -difference

More information

REAL ANALYSIS I HOMEWORK 3. Chapter 1

REAL ANALYSIS I HOMEWORK 3. Chapter 1 REAL ANALYSIS I HOMEWORK 3 CİHAN BAHRAN The quesions re from Sein nd Shkrchi s e. Chper 1 18. Prove he following sserion: Every mesurble funcion is he limi.e. of sequence of coninuous funcions. We firs

More information

Mathematics 805 Final Examination Answers

Mathematics 805 Final Examination Answers . 5 poins Se he Weiersrss M-es. Mhemics 85 Finl Eminion Answers Answer: Suppose h A R, nd f n : A R. Suppose furher h f n M n for ll A, nd h Mn converges. Then f n converges uniformly on A.. 5 poins Se

More information

ENGR 1990 Engineering Mathematics The Integral of a Function as a Function

ENGR 1990 Engineering Mathematics The Integral of a Function as a Function ENGR 1990 Engineering Mhemics The Inegrl of Funcion s Funcion Previously, we lerned how o esime he inegrl of funcion f( ) over some inervl y dding he res of finie se of rpezoids h represen he re under

More information

Weighted Inequalities for Riemann-Stieltjes Integrals

Weighted Inequalities for Riemann-Stieltjes Integrals Aville hp://pvm.e/m Appl. Appl. Mh. ISSN: 93-9466 ol. Ie Decemer 06 pp. 856-874 Applicion n Applie Mhemic: An Inernionl Jornl AAM Weighe Ineqliie or Riemnn-Sielje Inegrl Hüeyin Bk n Mehme Zeki Sriky Deprmen

More information

Analytic solution of linear fractional differential equation with Jumarie derivative in term of Mittag-Leffler function

Analytic solution of linear fractional differential equation with Jumarie derivative in term of Mittag-Leffler function Anlyic soluion of liner frcionl differenil equion wih Jumrie derivive in erm of Mig-Leffler funcion Um Ghosh (), Srijn Sengup (2), Susmi Srkr (2b), Shnnu Ds (3) (): Deprmen of Mhemics, Nbdwip Vidysgr College,

More information

Green s Functions and Comparison Theorems for Differential Equations on Measure Chains

Green s Functions and Comparison Theorems for Differential Equations on Measure Chains Green s Funcions nd Comprison Theorems for Differenil Equions on Mesure Chins Lynn Erbe nd Alln Peerson Deprmen of Mhemics nd Sisics, Universiy of Nebrsk-Lincoln Lincoln,NE 68588-0323 lerbe@@mh.unl.edu

More information

INTEGRALS. Exercise 1. Let f : [a, b] R be bounded, and let P and Q be partitions of [a, b]. Prove that if P Q then U(P ) U(Q) and L(P ) L(Q).

INTEGRALS. Exercise 1. Let f : [a, b] R be bounded, and let P and Q be partitions of [a, b]. Prove that if P Q then U(P ) U(Q) and L(P ) L(Q). INTEGRALS JOHN QUIGG Eercise. Le f : [, b] R be bounded, nd le P nd Q be priions of [, b]. Prove h if P Q hen U(P ) U(Q) nd L(P ) L(Q). Soluion: Le P = {,..., n }. Since Q is obined from P by dding finiely

More information

e t dt e t dt = lim e t dt T (1 e T ) = 1

e t dt e t dt = lim e t dt T (1 e T ) = 1 Improper Inegrls There re wo ypes of improper inegrls - hose wih infinie limis of inegrion, nd hose wih inegrnds h pproch some poin wihin he limis of inegrion. Firs we will consider inegrls wih infinie

More information

The Hadamard s inequality for quasi-convex functions via fractional integrals

The 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 information

A LIMIT-POINT CRITERION FOR A SECOND-ORDER LINEAR DIFFERENTIAL OPERATOR IAN KNOWLES

A LIMIT-POINT CRITERION FOR A SECOND-ORDER LINEAR DIFFERENTIAL OPERATOR IAN KNOWLES A LIMIT-POINT CRITERION FOR A SECOND-ORDER LINEAR DIFFERENTIAL OPERATOR j IAN KNOWLES 1. Inroducion Consider he forml differenil operor T defined by el, (1) where he funcion q{) is rel-vlued nd loclly

More information

AN INEQUALITY OF OSTROWSKI TYPE AND ITS APPLICATIONS FOR SIMPSON S RULE AND SPECIAL MEANS. I. Fedotov and S. S. Dragomir

AN 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 information

Integral inequalities for n times differentiable mappings

Integral 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 information

On the Pseudo-Spectral Method of Solving Linear Ordinary Differential Equations

On the Pseudo-Spectral Method of Solving Linear Ordinary Differential Equations Journl of Mhemics nd Sisics 5 ():136-14, 9 ISS 1549-3644 9 Science Publicions On he Pseudo-Specrl Mehod of Solving Liner Ordinry Differenil Equions B.S. Ogundre Deprmen of Pure nd Applied Mhemics, Universiy

More information

Refinements to Hadamard s Inequality for Log-Convex Functions

Refinements to Hadamard s Inequality for Log-Convex Functions Alied Mhemics 899-93 doi:436/m7 Pulished Online Jul (h://wwwscirporg/journl/m) Refinemens o Hdmrd s Ineuli for Log-Convex Funcions Asrc Wdllh T Sulimn Dermen of Comuer Engineering College of Engineering

More information

NEW 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. := 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 information

WENJUN LIU AND QUÔ C ANH NGÔ

WENJUN 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 information

New Integral Inequalities of the Type of Hermite-Hadamard Through Quasi Convexity

New 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 information

Some estimates on the Hermite-Hadamard inequality through quasi-convex functions

Some 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 information

HUI-HSIUNG KUO, ANUWAT SAE-TANG, AND BENEDYKT SZOZDA

HUI-HSIUNG KUO, ANUWAT SAE-TANG, AND BENEDYKT SZOZDA Communicions on Sochsic Anlysis Vol 6, No 4 2012 603-614 Serils Publicions wwwserilspublicionscom THE ITÔ FORMULA FOR A NEW STOCHASTIC INTEGRAL HUI-HSIUNG KUO, ANUWAT SAE-TANG, AND BENEDYKT SZOZDA Absrc

More information

f t f a f x dx By Lin McMullin f x dx= f b f a. 2

f t f a f x dx By Lin McMullin f x dx= f b f a. 2 Accumulion: Thoughs On () By Lin McMullin f f f d = + The gols of he AP* Clculus progrm include he semen, Sudens should undersnd he definie inegrl s he ne ccumulion of chnge. 1 The Topicl Ouline includes

More information

Temperature Rise of the Earth

Temperature Rise of the Earth Avilble online www.sciencedirec.com ScienceDirec Procedi - Socil nd Behviorl Scien ce s 88 ( 2013 ) 220 224 Socil nd Behviorl Sciences Symposium, 4 h Inernionl Science, Socil Science, Engineering nd Energy

More information

A Simple Method to Solve Quartic Equations. Key words: Polynomials, Quartics, Equations of the Fourth Degree INTRODUCTION

A Simple Method to Solve Quartic Equations. Key words: Polynomials, Quartics, Equations of the Fourth Degree INTRODUCTION Ausrlin Journl of Bsic nd Applied Sciences, 6(6): -6, 0 ISSN 99-878 A Simple Mehod o Solve Quric Equions Amir Fhi, Poo Mobdersn, Rhim Fhi Deprmen of Elecricl Engineering, Urmi brnch, Islmic Ad Universi,

More information

New general integral inequalities for quasiconvex functions

New 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 information

INEQUALITIES FOR TWO SPECIFIC CLASSES OF FUNCTIONS USING CHEBYSHEV FUNCTIONAL. Mohammad Masjed-Jamei

INEQUALITIES 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 information

Journal of Inequalities in Pure and Applied Mathematics

Journal 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 information

Journal of Inequalities in Pure and Applied Mathematics

Journal 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 information

An optimal 3-point quadrature formula of closed type and error bounds

An 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 information

Keywords : Generalized Ostrowski s inequality, generalized midpoint inequality, Taylor s formula.

Keywords : 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 information

Improvements of some Integral Inequalities of H. Gauchman involving Taylor s Remainder

Improvements of some Integral Inequalities of H. Gauchman involving Taylor s Remainder Divulgciones Mtemátics Vol. 11 No. 2(2003), pp. 115 120 Improvements of some Integrl Inequlities of H. Guchmn involving Tylor s Reminder Mejor de lguns Desigulddes Integrles de H. Guchmn que involucrn

More information

ON SOME NEW INEQUALITIES OF HADAMARD TYPE INVOLVING h-convex FUNCTIONS. 1. Introduction. f(a) + f(b) f(x)dx b a. 2 a

ON SOME NEW INEQUALITIES OF HADAMARD TYPE INVOLVING h-convex FUNCTIONS. 1. Introduction. f(a) + f(b) f(x)dx b a. 2 a Act Mth. Univ. Comenine Vol. LXXIX, (00, pp. 65 7 65 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

More information

On Two Integrability Methods of Improper Integrals

On Two Integrability Methods of Improper Integrals Inernaional Journal of Mahemaics and Compuer Science, 13(218), no. 1, 45 5 M CS On Two Inegrabiliy Mehods of Improper Inegrals H. N. ÖZGEN Mahemaics Deparmen Faculy of Educaion Mersin Universiy, TR-33169

More information

f (a) + f (b) f (λx + (1 λ)y) max {f (x),f (y)}, x, y [a, b]. (1.1)

f (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 information

How to Prove the Riemann Hypothesis Author: Fayez Fok Al Adeh.

How to Prove the Riemann Hypothesis Author: Fayez Fok Al Adeh. How o Prove he Riemnn Hohesis Auhor: Fez Fok Al Adeh. Presiden of he Srin Cosmologicl Socie P.O.Bo,387,Dmscus,Sri Tels:963--77679,735 Emil:hf@scs-ne.org Commens: 3 ges Subj-Clss: Funcionl nlsis, comle

More information

ON COMPANION OF OSTROWSKI INEQUALITY FOR MAPPINGS WHOSE FIRST DERIVATIVES ABSOLUTE VALUE ARE CONVEX WITH APPLICATIONS

ON 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 information

FM Applications of Integration 1.Centroid of Area

FM Applications of Integration 1.Centroid of Area FM Applicions of Inegrion.Cenroid of Are The cenroid of ody is is geomeric cenre. For n ojec mde of uniform meril, he cenroid coincides wih he poin which he ody cn e suppored in perfecly lnced se ie, is

More information

ON THE WEIGHTED OSTROWSKI INEQUALITY

ON 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 information

New Ostrowski Type Inequalities for Harmonically Quasi-Convex Functions

New Ostrowski Type Inequalities for Harmonically Quasi-Convex Functions X h Inernaional Saisics Days Conference (ISDC 206), Giresun, Turkey New Osrowski Tye Ineualiies for Harmonically Quasi-Convex Funcions Tuncay Köroğlu,*, İmda İşcan 2, Mehme Kun 3,3 Karadeniz Technical

More information

Bulletin of the. Iranian Mathematical Society

Bulletin 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 information

Procedia Computer Science

Procedia Computer Science Procedi Compuer Science 00 (0) 000 000 Procedi Compuer Science www.elsevier.com/loce/procedi The Third Informion Sysems Inernionl Conference The Exisence of Polynomil Soluion of he Nonliner Dynmicl Sysems

More information

ERROR ESTIMATES FOR APPROXIMATING THE FOURIER TRANSFORM OF FUNCTIONS OF BOUNDED VARIATION

ERROR ESTIMATES FOR APPROXIMATING THE FOURIER TRANSFORM OF FUNCTIONS OF BOUNDED VARIATION ERROR ESTIMATES FOR APPROXIMATING THE FOURIER TRANSFORM OF FUNCTIONS OF BOUNDED VARIATION N.S. BARNETT, S.S. DRAGOMIR, AND G. HANNA Absrc. I his pper we poi ou pproximio for he Fourier rsform for fucios

More information

Abstract. W.W. Memudu 1 and O.A. Taiwo, 2

Abstract. W.W. Memudu 1 and O.A. Taiwo, 2 Theoreicl Mhemics & Applicions, vol. 6, no., 06, 3-50 ISS: 79-9687 prin, 79-9709 online Scienpress d, 06 Eponenilly fied collocion pproimion mehod for he numericl soluions of Higher Order iner Fredholm

More information

Ostrowski Grüss Čebyšev type inequalities for functions whose modulus of second derivatives are convex 1

Ostrowski 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 information

Asymptotic relationship between trajectories of nominal and uncertain nonlinear systems on time scales

Asymptotic relationship between trajectories of nominal and uncertain nonlinear systems on time scales Asympoic relionship beween rjecories of nominl nd uncerin nonliner sysems on ime scles Fim Zohr Tousser 1,2, Michel Defoor 1, Boudekhil Chfi 2 nd Mohmed Djemï 1 Absrc This pper sudies he relionship beween

More information

Some Inequalities variations on a common theme Lecture I, UL 2007

Some Inequalities variations on a common theme Lecture I, UL 2007 Some Inequliies vriions on common heme Lecure I, UL 2007 Finbrr Hollnd, Deprmen of Mhemics, Universiy College Cork, fhollnd@uccie; July 2, 2007 Three Problems Problem Assume i, b i, c i, i =, 2, 3 re rel

More information

Journal of Mathematical Analysis and Applications. Two normality criteria and the converse of the Bloch principle

Journal of Mathematical Analysis and Applications. Two normality criteria and the converse of the Bloch principle J. Mh. Anl. Appl. 353 009) 43 48 Conens liss vilble ScienceDirec Journl of Mhemicl Anlysis nd Applicions www.elsevier.com/loce/jm Two normliy crieri nd he converse of he Bloch principle K.S. Chrk, J. Rieppo

More information

Research Article On New Inequalities via Riemann-Liouville Fractional Integration

Research 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 information

Solutions to Problems from Chapter 2

Solutions to Problems from Chapter 2 Soluions o Problems rom Chper Problem. The signls u() :5sgn(), u () :5sgn(), nd u h () :5sgn() re ploed respecively in Figures.,b,c. Noe h u h () :5sgn() :5; 8 including, bu u () :5sgn() is undeined..5

More information

How to prove the Riemann Hypothesis

How to prove the Riemann Hypothesis Scholrs Journl of Phsics, Mhemics nd Sisics Sch. J. Phs. Mh. S. 5; (B:5-6 Scholrs Acdemic nd Scienific Publishers (SAS Publishers (An Inernionl Publisher for Acdemic nd Scienific Resources *Corresonding

More information

Journal of Inequalities in Pure and Applied Mathematics

Journal 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 information

A Companion of Ostrowski Type Integral Inequality Using a 5-Step Kernel with Some Applications

A 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 information

Improvement of Grüss and Ostrowski Type Inequalities

Improvement of Grüss and Ostrowski Type Inequalities Filomt 9:9 (05), 07 035 DOI 098/FIL50907A Pulished y Fculty of Sciences nd Mthemtics, University of Niš, Seri Aville t: http://wwwpmfnicrs/filomt Improvement of Grüss nd Ostrowski Type Inequlities An Mri

More information

Chapter Direct Method of Interpolation

Chapter Direct Method of Interpolation Chper 5. Direc Mehod of Inerpolion Afer reding his chper, you should be ble o:. pply he direc mehod of inerpolion,. sole problems using he direc mehod of inerpolion, nd. use he direc mehod inerpolns o

More information

Citation Abstract and Applied Analysis, 2013, v. 2013, article no

Citation Abstract and Applied Analysis, 2013, v. 2013, article no Tile An Opil-Type Inequliy in Time Scle Auhor() Cheung, WS; Li, Q Ciion Arc nd Applied Anlyi, 13, v. 13, ricle no. 53483 Iued De 13 URL hp://hdl.hndle.ne/17/181673 Righ Thi work i licened under Creive

More information

The Hermite-Hadamard's inequality for some convex functions via fractional integrals and related results

The Hermite-Hadamard's inequality for some convex functions via fractional integrals and related results AMSI 4 No 69 The Herie-Hdrd' ineliy or oe conve ncion vi rcionl inegrl nd reled rel E SET M Z SARIKAYA M E ÖZDEMIR AND H YILDIRIM Arc In hi pper we elih Herie-Hdrd ype ineliie or conve ncion in he econd

More information

TEACHING STUDENTS TO PROVE BY USING ONLINE HOMEWORK Buma Abramovitz 1, Miryam Berezina 1, Abraham Berman 2

TEACHING STUDENTS TO PROVE BY USING ONLINE HOMEWORK Buma Abramovitz 1, Miryam Berezina 1, Abraham Berman 2 TEACHING STUDENTS TO PROVE BY USING ONLINE HOMEWORK Bum Armoviz 1, Mirym Berezin 1, Arhm Bermn 1 Deprmen of Mhemics, ORT Brude College, Krmiel, Isrel Deprmen of Mhemics, Technion IIT, Hf, Isrel Asrc We

More information

A Time Truncated Improved Group Sampling Plans for Rayleigh and Log - Logistic Distributions

A Time Truncated Improved Group Sampling Plans for Rayleigh and Log - Logistic Distributions ISSNOnline : 39-8753 ISSN Prin : 347-67 An ISO 397: 7 Cerified Orgnizion Vol. 5, Issue 5, My 6 A Time Trunced Improved Group Smpling Plns for Ryleigh nd og - ogisic Disribuions P.Kvipriy, A.R. Sudmni Rmswmy

More information

Fractional Calculus. Connor Wiegand. 6 th June 2017

Fractional Calculus. Connor Wiegand. 6 th June 2017 Frcionl Clculus Connor Wiegnd 6 h June 217 Absrc This pper ims o give he reder comforble inroducion o Frcionl Clculus. Frcionl Derivives nd Inegrls re defined in muliple wys nd hen conneced o ech oher

More information

On some inequalities for s-convex functions and applications

On 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 information

SOME 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 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 information

NEW FRACTIONAL DERIVATIVES WITH NON-LOCAL AND NON-SINGULAR KERNEL Theory and Application to Heat Transfer Model

NEW FRACTIONAL DERIVATIVES WITH NON-LOCAL AND NON-SINGULAR KERNEL Theory and Application to Heat Transfer Model Angn, A., e l.: New Frcionl Derivives wih Non-Locl nd THERMAL SCIENCE, Yer 216, Vol. 2, No. 2, pp. 763-769 763 NEW FRACTIONAL DERIVATIVES WITH NON-LOCAL AND NON-SINGULAR KERNEL Theory nd Applicion o He

More information

GENERALIZATIONS 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. (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 information

ON THE INEQUALITY OF THE DIFFERENCE OF TWO INTEGRAL MEANS AND APPLICATIONS FOR PDFs

ON THE INEQUALITY OF THE DIFFERENCE OF TWO INTEGRAL MEANS AND APPLICATIONS FOR PDFs ON THE INEQUALITY OF THE DIFFERENCE OF TWO INTEGRAL MEANS AND APPLICATIONS FOR PDFs A.I. KECHRINIOTIS AND N.D. ASSIMAKIS Deprtment of Eletronis Tehnologil Edutionl Institute of Lmi, Greee EMil: {kehrin,

More information

Hermite-Hadamard type inequalities for harmonically convex functions

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 information

DIFFERENCE BETWEEN TWO RIEMANN-STIELTJES INTEGRAL MEANS

DIFFERENCE 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 information

Hermite-Hadamard Type Inequalities for the Functions whose Second Derivatives in Absolute Value are Convex and Concave

Hermite-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 information

Approximation and numerical methods for Volterra and Fredholm integral equations for functions with values in L-spaces

Approximation and numerical methods for Volterra and Fredholm integral equations for functions with values in L-spaces Approximion nd numericl mehods for Volerr nd Fredholm inegrl equions for funcions wih vlues in L-spces Vir Bbenko Deprmen of Mhemics, The Universiy of Uh, Sl Lke Ciy, UT, 842, USA Absrc We consider Volerr

More information

3. Renewal Limit Theorems

3. Renewal Limit Theorems Virul Lborories > 14. Renewl Processes > 1 2 3 3. Renewl Limi Theorems In he inroducion o renewl processes, we noed h he rrivl ime process nd he couning process re inverses, in sens The rrivl ime process

More information

ON AN INTEGRATION-BY-PARTS FORMULA FOR MEASURES

ON 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 information

Communications inmathematicalanalysis Volume 6, Number 2, pp (2009) ISSN

Communications inmathematicalanalysis Volume 6, Number 2, pp (2009) ISSN Communictions inmthemticlanlysis Volume 6, Number, pp. 33 41 009) ISSN 1938-9787 www.commun-mth-nl.org A SHARP GRÜSS TYPE INEQUALITY ON TIME SCALES AND APPLICATION TO THE SHARP OSTROWSKI-GRÜSS INEQUALITY

More information

An integral having either an infinite limit of integration or an unbounded integrand is called improper. Here are two examples.

An integral having either an infinite limit of integration or an unbounded integrand is called improper. Here are two examples. Improper Inegrls To his poin we hve only considered inegrls f(x) wih he is of inegrion nd b finie nd he inegrnd f(x) bounded (nd in fc coninuous excep possibly for finiely mny jump disconinuiies) An inegrl

More information

September 20 Homework Solutions

September 20 Homework Solutions College of Engineering nd Compuer Science Mechnicl Engineering Deprmen Mechnicl Engineering A Seminr in Engineering Anlysis Fll 7 Number 66 Insrucor: Lrry Creo Sepember Homework Soluions Find he specrum

More information

arxiv: v1 [math.ca] 28 Jan 2013

arxiv: 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 information

MTH 146 Class 11 Notes

MTH 146 Class 11 Notes 8.- Are of Surfce of Revoluion MTH 6 Clss Noes Suppose we wish o revolve curve C round n is nd find he surfce re of he resuling solid. Suppose f( ) is nonnegive funcion wih coninuous firs derivive on he

More information