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    Comparing the Estimation Methods of Stable Distributions with Respect to Robustness Properties
    (Amer Inst Physics, 2016) Çelik, Nuri; Erden, Samet; Sarıkaya, Mehmet Zeki
    In statistical applications, some data set may exhibit the features like high skewness and kurtosis and heavy tailness that are incompatible with the normality assumption especially in finance and engineering. For these reason, the modeling of the data sets with alpha stable distributions will be reasonable approach. The stable distributions have four parameters. In literature, the estimation methods have been studied in order to estimate these unknown model parameters. In this study, we give small information about these proposed estimation methods and we compare these estimators with respect to robustness properties with a comprehensive simulation study, since the robustness property of an estimator has been an important tool for an appropriate modeling.
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    Fractional Ostrowski type inequalities for bounded functions
    (Springer, 2020) Erden, Samet; Budak, Huseyin; Zeki Sarikaya, Mehmet; Iftikhar, Sabah; Kumam, Poom
    We first establish some results involving Riemann-Liouville fractional integrals for partially differentiable functions. Then we obtain some fractional Ostrowski type inequalities for functions in class of functions Lp, L-infinity and L-1, respectively. We also give some midpoint type inequalities as special cases of our main results.
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    A GENERALIZED AND REFINED PERTURBED VERSION OF OSTROWSKI TYPE INEQUALITIES
    (Etamaths Publ, 2017) Sarıkaya, Mehmet Zeki; Budak, Hüseyin; Erden, Samet; Qayyum, Ather
    In this paper, we first obtain a new identity for twice differentiable mappings. Then, we establish generalized and improved perturbed version of Ostrowski type inequalities for functions whose derivatives are of bounded variation or second derivatives are either bounded or Lipschitzian.
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    Generalized Pompeiu type inequalities for local fractional integrals and its applications
    (Elsevier Science Inc, 2016) Erden, Samet; Sarıkaya, Mehmet Zeki
    First of all, the generalized Pompeius mean value theorem is established. Then, some generalized Pompeiu type inequalities are obtained. Finally, some applications of these inequalities in numerical integration and for special means are given. (C) 2015 Elsevier Inc. All rights reserved.
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    GENERALIZED POWER POMPEIU TYPE INEQUALITIES FOR LOCAL FRACTIONAL INTEGRALS WITH APPLICATIONS TO OSTROWSKI'S INEQUALITY
    (Turkic World Mathematical Soc, 2019) Erden, Samet; Sarıkaya, Mehmet Zeki; Dragomir, Silvestru Sever
    We establish some generalizations of power Pompeiu's inequality for local fractional integral. Afterwards, these results gave some new generalized Ostrowski type inequalities. Finally, some applications of these inequalities for generalized special means are obtained.
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    GENERALIZED STEFFENSEN INEQUALITIES FOR LOCAL FRACTIONAL INTEGRALS
    (Etamaths Publ, 2017) Sarıkaya, Mehmet Zeki; Tunç, Tuba; Erden, Samet
    Firstly we give a important integral inequality which is generalized Steffensen's inequality. Then, we establish weighted version of generalized Steffensen's inequality for local fractional integrals. Finally, we obtain several inequalities related these inequalities using the local fractional integral.
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    Gruss type inequalities for generalized fractional integrals
    (Amer Inst Physics, 2016) Erden, Samet; Sarıkaya, Mehmet Zeki; Budak, Hüseyin
    In this study, some Gruss type inequalities for generalized fractional integrals are presented. Also, the results presented here would provide extensions of those given in earlier works.
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    Hermite-Hadamard, Trapezoid and Midpoint Type Inequalities Involving Generalized Fractional Integrals for Convex Functions
    (Univ Maragheh, 2023) Kara, Hasan; Erden, Samet; Budak, Hüseyin
    We first construct new Hermite-Hadamard type in-equalities which include generalized fractional integrals for convex functions by using an operator which generates some significant fractional integrals such as Riemann-Liouville fractional and the Hadamard fractional integrals. Afterwards, Trapezoid and Mid-point type results involving generalized fractional integrals for func-tions whose the derivatives in modulus and their certain powers are convex are established. We also recapture the previous results in the particular situations of the inequalities which are given in the earlier works.
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    İki katlı integraller için bazı genelleşmiş eşitsizlikler ve uygulamalar
    (Düzce Üniversitesi, 2017) Erden, Samet; Sarıkaya, Mehmet Zeki
    Bu tezin başlıca amacı, iki katlı integralleri kullanarak koordinatlara göre konveks veya farklı tipte sınırlı fonksiyonlar için Hermite-Hadamard tipli ve Ostrowski tipli eşitsizlikler kurmaktır. Bölüm 3'te, ilk olarak ikinci mertebeden kısmi türevli fonksiyonlar için bir özdeşlik kurulmuştur. Daha sonra, bu özdeşliği kullanılarak iki katlı integraller için yeni Ostrowski tipli eşitsizlikler elde edilmiştir. Aynı zamanda, bu Ostrowski tipli eşitsizliklerin Cubature formülü ile bağlantılı bazı uygulamaları verilmiştir. Son olarak, kısmi türevlerinin mutlak değeri koordinatlara göre konveks olan fonksiyonların iki katlı integralleri için Hermite-Hadamard tipli eşitsizlikler incelenmiştir. Bölüm 4'te, dikdörtgensel bir bölgede tanımlı koordinatlar üzerinde konveks olan fonksiyonlar için genelleştirilmiş ağırlıklı integral eşitsizilikleri verilmiştir. Bu sonuçlar kısmi türevlerinin mutlak değerleri konveks olan fonksiyonlar için elde edilen güncel sonuçları genelleştirmektedir. Bölüm 5'te, Lebesgue uzaylarına ait iki boyutlu integraller kullanılarak yüksek mertebeden kısmi türevler içeren ağırlıklı Ostrowski tipli eşitsizlikler kurulmuştur. Daha sonra, bu sonuçlar Cubature formülüne uygulanmıştır. Ek olarak, bu eşitsizlikler yardımıyla rasgele değişkenlerin momentleri üzerine uygulamalar verilmiştir. Son olarak, iki katlı integraller kullanılarak her mertebeden kısmi türevleri koordinatlara göre konveks olan fonksiyonlar için ağırlıklı Hadamard tipli eşitsizlikler elde edilmiştir.
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    New bounds for q-midpoint-type inequalities via twice q-differentiable functions on quantum calculus
    (Springer, 2022) Alp, Necmettin; Budak, Hüseyin; Erden, Samet; Sarıkaya, Mehmet Zeki
    The aim of this work is to establish new bounds for q-midpoint-type integral inequalities for twice q-differentiable convex functions. We first prove some lemmas which are useful for our main results. Then, we present some midpoint-type inequalities for twice q-differentiable functions. With all these, we showed the results we found in the classical analysis by using q -> 1(-).
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    New Weighted Inequalities for Higher Order Derivatives and Applications
    (Univ Nis, Fac Sci Math, 2018) Erden, Samet; Sarıkaya, Mehmet Zeki; Budak, Hüseyin
    We establish a new Ostrowski type inequality for (n + 1)-times differentiable mappings which are bounded. Then, some new inequalities of Hermite-Hadamard type are obtained for functions whose (n + 1) th derivatives in absolute value are convex. Spacial cases of these inequalities reduce some well known inequalities. With the help of obtained inequalities, we give applications for the kth-moment of random variables.
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    NEW WEIGHTED INTEGRAL INEQUALITIES FOR TWICE DIFFERENTIABLE CONVEX FUNCTIONS
    (Univ Kragujevac, Fac Science, 2016) Sarıkaya, Mehmet Zeki; Erden, Samet
    In this paper, we establish several new weighted inequalities for some twice differentiable mappings that are connected with the celebrated Hermite-Hadamard type and Ostrowski type integral inequalities. Some of the new inequalities are Hermite-Hadamard-type inequalities involving fractional integrals. The results presented here would provide extensions of those given in earlier works.
  • Küçük Resim Yok
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    NEW WEIGHTED OSTROWSKI TYPE INEQUALITIES FOR MAPPINGS WHOSE nTH DERIVATIVES ARE OF BOUNDED VARIATION
    (Etamaths Publ, 2016) Budak, Hüseyin; Erden, Samet; Sarıkaya, Mehmet Zeki
    We establish a new generalization of weighted Ostrowski type inequality for mappings of bounded variation. Spacial cases of this inequality reduce some well known inequalities. With the help of obtained inequality, we give applications for the kth moment of random variables.
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    On Fejer Type Inclusions for Products of Interval-Valued Convex Functions
    (Univ Nis, Fac Sci Math, 2021) Budak, Hüseyin; Kara, Hasan; Erden, Samet
    We first get some new Fejer type inclusions for products of interval-valued convex mappings. The most important feature of our work is that it contains Fejer type inclusions for both interval-valued integrals and interval-valued fractional integrals.
  • Küçük Resim Yok
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    ON GENERALIZED SOME INEQUALITIES FOR CONVEX FUNCTIONS
    (Forum Editrice Univ Udinese, 2017) Erden, Samet; Sarıkaya, Mehmet Zeki
    In this paper, a general integral identity for differentiable mapping is derived. Then, we extend some estimates of the right hand and left hand side of a HermiteHadamard-Fejer type inequality for functions whose first derivatives absolute values are convex. Some applications for special means of real numbers are also provided. The results presented here would provide extensions of those given in earlier works.
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    ON NEW INEQUALITIES OF SIMPSON'S TYPE FOR GENERALIZED CONVEX FUNCTIONS
    (Kangwon-Kyungki Mathematical Soc, 2019) Sarıkaya, Mehmet Zeki; Budak, Hüseyin; Erden, Samet
    In this paper, using local fractional integrals on fractal sets R-alpha (0 < alpha <= 1) of real line numbers, we establish new some inequalities of Simpson's type based on generalized convexity.
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    On some new midpoint inequalities for the functions of two variables via quantum calculus
    (Springer, 2021) You, Xuexiao; Ali, Muhammad Aamir; Erden, Samet; Budak, Huseyin; Chu, Yu-Ming
    In this paper, first we obtain a new identity for quantum integrals, the result is then used to prove midpoint type inequalities for differentiable coordinated convex mappings. The outcomes provided in this article are an extension of the comparable consequences in the literature on the midpoint inequalities for differentiable coordinated convex mappings.
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    ON THE GENERALIZED INTEGRAL INEQUALITIES FOR TWICE DIFFERENTIABLE MAPPINGS
    (Yildiz Technical Univ, 2019) Sarıkaya, Mehmet Zeki; Erden, Samet; Budak, Hüseyin
    In this paper, an important integral equality is derived. Then, we establish several new inequalities for some twice differentiable mappings that are connected with the celebrated Hermite-Hadamard type and Ostrowski type integral inequalities. Some of the new inequalities are obtained by using Gruss inequality and Chebyshev inequality. The results presented here would provide extensions of those given in earlier works
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    On the weighted integral inequalities for convex function
    (Sapientia University, 2014) Sarıkaya, Mehmet Zeki; Erden, Samet
    In this paper, we establish several weighted inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard-Fejér type and Ostrowski type integral inequalities. The results presented here would provide extensions of those given in earlier works.
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    On the weighted Ostrowski type inequalities for double integrals
    (University of Kragujevac, Faculty of Science, 2014) Sarıkaya, Mehmet Zeki; Yaldız, Hatice; Erden, Samet
    In this paper, we obtain weighted Ostrowski type inequalities for function whose second order partial derivatives are bounded.