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Some New Inequalities for Lipschitz Functions via a Functional

Year 2019, Volume: 9 Issue: 2, 301 - 306, 15.04.2019
https://doi.org/10.17714/gumusfenbil.436723

Abstract

This study is about getting some new integral
inequalities for Lipschitz functions by using a functional defined via a
Lipschitz function. Here, some new Hermite-Hadamard (H-H) type inequalities are
first found out as a corollary of main theorems. Afterwards, some new H-H type
inequalities for Lipschitz functions by means of inequalities which are used
for
-convex functions are obtained.

References

  • 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.
  • 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.
  • 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.
  • 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.
  • İşcan, İ., 2014, Hermite-Hadamard type inequalities for harmonically convex functions. Hacettepe Journal of Mathematics and Statistics, 43(6), 935-942.
  • İşcan, İ., 2016, Ostrowski type inequalities for p-convex functions, New Trends in Mathematical Sciences, NTMSCI 4, No. 3, 140-150.
  • 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.
  • 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.
  • Kunt, M. and İşcan, İ., 2017b, Hermite-Hadamard-Fejer type inequalities for p-convex functions, Arab J. Math. Sci., 23(2), 215-230.
  • 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.
  • 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.
  • 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.
  • Niculescu, C.P., 2000, Convexity according to the geometric mean. Math. Inequal. Appl., 3(2):155-167. 10.7153/mia-03-19.
  • Pečarić, J., Proschan, F. and Tong, Y. L., 1992, Convex Functions, Partial Orderings and Statistical Applications. Academic Press, Inc., 469 pp, Boston.
  • Roberts, A.W. and Varberg, D.E., 1973, Convex Functions. Academic Press, 300 pp, New York.
  • Yang, G.S. and Tseng, K.L., 1999, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239, 180-187.

Bir Fonksiyonel yardımı ile Lipschitz Fonksiyonları için Bazı Yeni Eşitsizlikler

Year 2019, Volume: 9 Issue: 2, 301 - 306, 15.04.2019
https://doi.org/10.17714/gumusfenbil.436723

Abstract

Bu çalışma, bir
Lipschitz fonksiyonu yardımı ile tanımlanmış bir fonksiyonel kullanarak
Lipschitz fonksiyonları için bazı yeni integral eşitsizliklerin elde edilmesi
ile ilgilidir. Burada ilk önce, bazı yeni Hermite-Hadamard tipi eşitsizlikler,
ana teoremlerin bir sonucu olarak ortaya çıkarılacaktır. Daha sonra ise,
-konveks
fonksiyonlar için kullanılan eşitsizlikler aracılığıyla Lipschitz fonksiyonları
için yeni Hermite Hadamard tipi eşitsizlikler elde edilecektir.

References

  • 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.
  • 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.
  • 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.
  • 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.
  • İşcan, İ., 2014, Hermite-Hadamard type inequalities for harmonically convex functions. Hacettepe Journal of Mathematics and Statistics, 43(6), 935-942.
  • İşcan, İ., 2016, Ostrowski type inequalities for p-convex functions, New Trends in Mathematical Sciences, NTMSCI 4, No. 3, 140-150.
  • 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.
  • 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.
  • Kunt, M. and İşcan, İ., 2017b, Hermite-Hadamard-Fejer type inequalities for p-convex functions, Arab J. Math. Sci., 23(2), 215-230.
  • 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.
  • 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.
  • 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.
  • Niculescu, C.P., 2000, Convexity according to the geometric mean. Math. Inequal. Appl., 3(2):155-167. 10.7153/mia-03-19.
  • Pečarić, J., Proschan, F. and Tong, Y. L., 1992, Convex Functions, Partial Orderings and Statistical Applications. Academic Press, Inc., 469 pp, Boston.
  • Roberts, A.W. and Varberg, D.E., 1973, Convex Functions. Academic Press, 300 pp, New York.
  • Yang, G.S. and Tseng, K.L., 1999, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239, 180-187.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mahir Kadakal 0000-0002-0240-918X

İmdat İşcan 0000-0001-6749-0591

Cuma Altunsoy This is me 0000-0003-1865-9842

Publication Date April 15, 2019
Submission Date June 25, 2018
Acceptance Date October 10, 2018
Published in Issue Year 2019 Volume: 9 Issue: 2

Cite

APA Kadakal, M., İşcan, İ., & Altunsoy, C. (2019). Bir Fonksiyonel yardımı ile Lipschitz Fonksiyonları için Bazı Yeni Eşitsizlikler. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 9(2), 301-306. https://doi.org/10.17714/gumusfenbil.436723