PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR TWICE DIFFERENTIABLE FUNCTIONS

In this paper, some perturbed companion of Ostrowski type integral inequalities for functions whose second derivatives are either bounded or of bounded variation are established

Some inequalities associated with fractional integrals

YÖK Tez No: 436316Kesirli türev ve kesirli integral kavramları ilk olarak Liouville tarafından ortaya atıldı. Bu fikrin temel kaynağı; kesirli türev ve kesirli integral kavramı türev ve integrallerin sadece tamsayılar için var mıdır sorusundan yola çıkılarak ortaya çıkmıştır. Daha sonra Euler kesirli türevi yeniden ele aldı ve 17. yüzyıldan itibaren Leibniz, Euler, Lagrange, Abel, Liouville ve diğer birçok matematikçinin, kesirli mertebe için diferansiyel ve integrasyonun genelleştirilmesine dayanan öncü çalışmalarıyla gelişmeye başlanmıştır. Keyfi mertebeli diferansiyel ve integrasyon kavramları, tamsayı mertebeli türev ve n-katlı integralleri birleştiren ve genelleştiren kavramlardır. Buradan hareketle, bu tez dört bölümden oluşmaktadır. İlk bölümde, kesirli integraller hakkında genel bilgiler verilip daha sonra temel kavramlardan bahsedilecektir. İkinci bölümde kesirli integraller hakkında bilgiler verilecek olup; kesirli integral ve kesirli türevin elde edilişi ve bu konu hakkındaki çözüm yöntemleri, üçüncü bölümde ise, eldeki verilerden yararlanılarak üç başlık altında toplanan bulgular, son bölümde ise, sonuçlar ve öneriler verilecektir.Fractional derivatives and fractional integral notions were first raised by Liouville. The main source of this idea; fractional derivatives and fractional integral concept has emerged from the question: "Is there derivatives and integrals for only integers." Then, Euler dealt with fractional derivatives again and Leibniz, Euler, Lagrange, Abel, Liouville and many other mathematicians have begun to develop the fractional derivatives since 17th century as their pioneering work based on differential and integration to be generalized to fractional order. Arbitrary order differential and integration concepts are the notions which combine and generalize integer-order derivatives and n-fold integrals. Thus, this thesis consists of four chapters. In the first chapter, of how the concepts of fractional integral and fractional derivative is given. In the second chapter, all the necessary definitions and basic theorems for this study have been given. The third section, benefiting from the available data the findings summarized under three headings are given. In the fourth chapter, results and recommendations will be given

Hermite -Hadamard's inequalities for fractional integrals

YÖK Tez No: 346412Bu tez dört bölümden oluşmaktadır. Birinci bölümde, kesirli integral ve kesirli türev kavramlarının nasıl oluştuğu verildi. İkinci bölümde,çalışmamız için gerekli olan tanım ve temel teoremler verildi. Üçüncü bölümde, kesirli integraller ve kesirli türevlerin elde edilişi ve bu konu hakkındaki çözüm yöntemleri verildi. Dördüncü bölümde, Hermite-Hadamard tipli eşitsizliğe kesirli integrallerin uygulanması elde edildi.Anahtar sözcükler: Kesirli İntegraller ve Kesirli Türevler, Hermite-Hadamard Eşitsizliği, Konveks Fonksiyonlar.This thesis consists of four chapters. In the first chapter, of how the concepts of fractional integral and fractional derivative is given. In the second chapter, all the necessary definitions and basic theorems for this study have been given. The third section, the derivation of the fractional integrals and fractional derivatives and methods of solution on this issue are given. In the fourth chapter, the implementation of the Hermite-Hadamard-type inequalities for fractional integrals are obtained

On Hermite-Hadamard type inequalities via Katugampola fractional integrals

In this paper, we give new definitons related to Katugampola fractional integral for two variables functions. We are interested in giving the Hermite–Hadamard inequality for a rectangle in plane via convex functions on co-ordinates involving Katugampola fractional integral.Publisher's Versio

Some new ostrowski type inequalities for generalized fractional integrals

1st International Conference On Mathematical And Related Sciences (Icmrs) -- Apr 30-May 04, 2018 -- Antalya, TurkeyWOS:000450569900018In this paper, we extend the Montgomery identities for the generalized fractional integrals. These results are connected with the celebrated Ostrowski type integral inequality for generalized fractional integral operators by definition of Sarikaya et al.[6]. The results presented here would provide extensions of those given in earlier works.Düzce Uni

S-convex functions on discrete time domains

In the present work, we give the definition of an s-convex functions for a convex real-valued function f defined on the set of integers ?. We state and prove the discrete Hermite-Hadamard inequality for s-convex functions by using the basics of discrete calculus (i.e. the calculus on ?). Finally, we state and prove the discrete fractional Hermite-Hadamard inequality for s-convex functions by using the basics of discrete fractional calculus. © 2017 Walter de Gruyter GmbH, Berlin/Boston 2017

On weighted Montgomery identity for Riemann-Liouville fractional integrals

In this paper, we extend the weighted Montogomery identity for the Riemann-Liouville fractional integral. We also use this Montogomery identity to establish some new weighted Ostrowski type integral inequalities. © 2014, Publishing House of the Romanian Academy. All rights reserved

On hermite-hadamard type inequalities for ?-convex functions via fractional integrals

In this paper, we establish integral inequalities of Hermite-Hadamard type involving Riemann-Liouville fractional integrals for ? -convex functions and some new inequalities of right-hand side of Hermite-Hadamard type are given for functions whose first derivatives absolute values ? -convex functions via Riemann-Liouville fractional integrals

On Hermite-Hadamard Type Inequalities for phi-convex Functions via Fractional Integrals

WOS: 000436729300005In this paper, we establish integral inequalities of Hermite-Hadamard type involving Riemann-Liouville fractional integrals for phi-convex functions and some new inequalities of right-hand side of Hermite-Hadamard type are given for functions whose first derivatives absolute values phi-convex functions via Riemann-Liouville fractional integrals

Refinements on the discrete Hermite–Hadamard inequality

Abstract In this paper, we use techniques and tools from time scale calculus to state and prove many refinements on the discrete Hermite–Hadamard inequality