TY  - JOUR
T1  - Bir Fonksiyonel yardımı ile Lipschitz Fonksiyonları için Bazı Yeni Eşitsizlikler
TT  - Some New Inequalities for Lipschitz Functions via a Functional
AU  - Kadakal, Mahir
AU  - İşcan, İmdat
AU  - Altunsoy, Cuma
PY  - 2019
DA  - April
Y2  - 2018
DO  - 10.17714/gumusfenbil.436723
JF  - Gümüşhane Üniversitesi Fen Bilimleri Dergisi
PB  - Gümüşhane Üniversitesi
WT  - DergiPark
SN  - 2146-538X
SP  - 301
EP  - 306
VL  - 9
IS  - 2
LA  - en
AB  - Bu çalışma, birLipschitz fonksiyonu yardımı ile tanımlanmış bir fonksiyonel kullanarakLipschitz fonksiyonları için bazı yeni integral eşitsizliklerin elde edilmesiile ilgilidir. Burada ilk önce, bazı yeni Hermite-Hadamard tipi eşitsizlikler,ana teoremlerin bir sonucu olarak ortaya çıkarılacaktır. Daha sonra ise, -konveksfonksiyonlar için kullanılan eşitsizlikler aracılığıyla Lipschitz fonksiyonlarıiçin yeni Hermite Hadamard tipi eşitsizlikler elde edilecektir.
KW  - Konveks fonksiyon
KW  - Lipschitz fonksiyonu
KW  - p-konveks fonksiyon
N2  - This study is about getting some new integralinequalities for Lipschitz functions by using a functional defined via aLipschitz function. Here, some new Hermite-Hadamard (H-H) type inequalities arefirst found out as a corollary of main theorems. Afterwards, some new H-H typeinequalities for Lipschitz functions by means of inequalities which are usedfor -convex functions are obtained.
CR  - Dragomir, S.S. Cho, Y.J. and Kim, S.S., 2000, Inequalities of Hadamard's type for Lipschitzian mappings and their applications, Journal of Mathematical Analysis and Applications, vol. 245, no. 2, pp. 489-501.
CR  - Dragomir, S.S., Pearce, C.E.M., 2002, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monograph, Victoria University, online:http://rgmia.org/monographs.php.
CR  - Dragomir, S.S., 2002, On Some New inequalities of Hermite-Hadamrd Type for m-Convex Functions, Tamkang J. of Math., vol. 33, 1, 45-55.
CR  - Hadamard, J., 1893,  Etude sur les proprietes des fonctions entieres en particulier d'une fonction consideree par Riemann, J. Math. Pures Appl. 58, 171-215.
CR  - İşcan, İ., 2014, Hermite-Hadamard type inequalities for harmonically convex functions. Hacettepe Journal of Mathematics and Statistics, 43(6), 935-942.
CR  - İşcan, İ., 2016,  Ostrowski type inequalities for p-convex functions, New Trends in Mathematical Sciences, NTMSCI 4, No. 3, 140-150.
CR  - İşcan, İ., Altunsoy, C. and Kadakal, M., 2018, New inequalities on Lipschitz functions, International Conference on Mathematics and Mathematics Education, Ordu University, Ordu, 27-29 Haziran,  Book of abstracts, s.169.
CR  - Kunt, M. and İşcan, İ., 2017a, On new Hermite-Hadamard-Fejer type inequalities for p-convex functions via fractional integrals, Communication in Mathematical Modeling and Applications, Volume: 2, Issue: 1, June, pp:1-15.
CR  - Kunt, M. and İşcan, İ., 2017b, Hermite-Hadamard-Fejer type inequalities for p-convex functions, Arab J. Math. Sci., 23(2), 215-230.
CR  - Kunt, M. and İşcan, İ., 2017c, Hermite-Hadamard-Fejer type inequalities for p-convex functions via fractional integrals, Iranian Journal of Science and Technology, Transactions A: Science, Doi:10.1007/s40995-017-0352-4.
CR  - Kunt, M. and İşcan, İ., 2017d, Hermite-Hadamard type inequalities for p-convex functions via fractional integrals, Moroccan J. Pure Appl. Anal., 3(1), 22-35.
CR  - Latif, M.A. Dragomir S. S. and Momaniat, E., 2015, Some Fejer type integral inequalities for geometrically-arithmetically-convex functions with applications, RGMIA Research Report Collection, 18, Article 25, 18 pp.
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CR  - Pečarić, J., Proschan, F. and Tong, Y. L., 1992, Convex Functions, Partial Orderings and Statistical Applications. Academic Press, Inc., 469 pp, Boston.
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CR  - Yang, G.S. and Tseng, K.L., 1999, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239, 180-187.
UR  - https://doi.org/10.17714/gumusfenbil.436723
L1  - https://dergipark.org.tr/tr/download/article-file/692665
ER  -