Research Article
BibTex RIS Cite
Year 2020, Volume: 24 Issue: 4, 665 - 674, 01.08.2020
https://doi.org/10.16984/saufenbilder.711507

Abstract

References

  • [1] G. A. Anastassiou, “Complex Multivariate Montgomery Type Identity Leading to Complex Multivariate Ostrowski and Grüss Inequalities”, Communications in Advanced Mathematical Sciences, vol. II, no. 2, pp. 161-175, 2019.
  • [2] W. W. Breckner, "Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Räumen", Publ. Inst. Math., vol. 23, pp. 13–20, 1978.
  • [3] K. Bekar, "Hermite-Hadamard type inequalities for trigonometrically P-functions", Comptes rendus de l’Académie bulgare des Sciences, vol. 72, no. 11, pp. 1449-1457, 2019.
  • [4] H. Budak, F. Usta and M. Z. Sarikaya, “Refinements of the Hermite–Hadamard inequality for coordinated convex mappings”, Journal of Applied Analysis, vol. 25, no. 1, pp. 73-81, 2019.
  • [5] H. Budak, F. Usta, M. Z. Sarikaya, M. E. Ozdemir, “On generalization of midpoint type inequalities with generalized fractional integral operators”, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, vol. 113, no. 2, pp. 769-790, 2019.
  • [6] H. Budak, F. Usta, “New Upper Bounds of Ostrowski Type Integral Inequalities Utilizing Taylor Expansion”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 3, pp. 567-578, 2018.
  • [7] S. S. Dragomir, C. E. M. Pearce, "Selected Topics on Hermite-Hadamard Inequalities and Applications", RGMIA Monographs, Victoria University, 2000.
  • [8] S. S. Dragomir, J. Pecaric, L. E. Persson, "Some inequalities of Hadamard Type", Soochow Journal of Mathematics, vol. 21, no. 3, pp. 335–341, 2001.
  • [9] S. S. Dragomir, Th. M. Rassias, "Ostrowski type inequalities and applications in numerical integration", Kluwer Academic Publishers, Dorcdrecht, Boston, London, 2002.
  • [10] İ. İşcan, New estimates on generalization of some integral inequalities for s-convex functions and their applications, Int. J. Pure Appl. Math., vol. 86, no. 4, pp. 727-746, 2013.
  • [11] H. Kadakal, "Hermite–Hadamard type inequalities for trigonometrically convex functions", Scientific Studies and Research. Series Mathematics and Informatics, vol. 28, no. 2, pp. 19–28, 2018.
  • [12] M. Kadakal, İ. İşcan, Inequalities of Hermite-Hadamard and Bullen Type for AH -Convex Functions. Universal Journal of Mathematics and Applications, vol. 2, no. 3, pp. 152-158, 2019.
  • [13] M. Kadakal, “Better Results for Trigonometrically Convex Functions via Hölder-İşcan and Improved Power-Mean Inequalities”, Universal Journal of Mathematics and Applications, vol. 3, no. 1, pp. 38-43, 2020.
  • [14] M. Z. Sarikaya, E. Set, M. E. Özdemir, "On new inequalities of Simpson’s type for convex functions", Computers & Mathematics with Applications, vol. 60, no. 8, pp. 2191-2199, 2010.
  • [15] M. Z. Sarikaya, N. Aktan, "On the generalization of some integral inequalities and their applications", Mathematical and Computer Modelling, vol. 54, no. 9-10, pp. 2175-2182, 2011.
  • [16] F. Usta, M. Z. Sarıkaya, “Explicit Bounds on Certain Integral Inequalities via Conformable Fractional Calculus, Cogent Mathematics, vol. 4, no. 1, 1277505, 2017.
  • [17] F. Usta, “On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators”, Filomat, vol. 32, no. 6, 2018.
  • [18] F. Usta, M. Z. Sarıkaya, “On Generalization of Pachpatte Type Inequalities for Conformable Fractional Integral, TWMS Journal of Applied and Engineering Mathematics, vol. 8, no. 1, 106, 2018.
  • [19] F. Usta, M. Z. Sarıkaya, “On Bivariate Retarded Integral Inequalities and Their Applications” Facta Universitatis, Series: Mathematics and Informatics, vol. 34, no. 3, pp. 553-561, 2019.
  • [20] F. Usta, H. Budak, M. Z. Sarıkaya, “Montgomery Identities and Ostrowski type Inequalities for Fractional Integral Operators”, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, vol. 113, no. 2, pp. 1059-1080, 2019.
  • [21] F. Usta, H. Budak, F. Ertuğral, M. Z. Sarıkaya, “The Minkowski’s Inequalities Utilizing Newly Defined Generalized Fractional Integral Operators, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, pp. 686-701, 2019.
  • [22] F. Usta, H. Budak, M. Z. Sarıkaya, “Some New Chebyshev Type Inequalities Utilizing Generalized Fractional Integral Opetors”, AIMS Mathematics, vol. 5, no. 2, 2020.
  • [23] S. Varošanec, "On h-convexity", J. Math. Anal. Appl., vol. 326, no. 1, pp. 303–311, 2007.

Novel Results based on Generalisation of Some Integral Inequalities for Trigonometrically -P Function

Year 2020, Volume: 24 Issue: 4, 665 - 674, 01.08.2020
https://doi.org/10.16984/saufenbilder.711507

Abstract

Trigonometric P-function is defined as a special case of h-convex function. In this article, we used a general lemma that gives trapezoidal, midpoint, Ostrowski, and Simpson type inequalities. With the help of this lemma, we have obtained many integral inequalities and generalisations for trigonometric P-function. We have shown that it goes down to the studies in special cases which are described in our study. Apart from that, we got new results for the trapezoidal, midpoint, Ostrowski, and Simpson type inequalities.

References

  • [1] G. A. Anastassiou, “Complex Multivariate Montgomery Type Identity Leading to Complex Multivariate Ostrowski and Grüss Inequalities”, Communications in Advanced Mathematical Sciences, vol. II, no. 2, pp. 161-175, 2019.
  • [2] W. W. Breckner, "Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Räumen", Publ. Inst. Math., vol. 23, pp. 13–20, 1978.
  • [3] K. Bekar, "Hermite-Hadamard type inequalities for trigonometrically P-functions", Comptes rendus de l’Académie bulgare des Sciences, vol. 72, no. 11, pp. 1449-1457, 2019.
  • [4] H. Budak, F. Usta and M. Z. Sarikaya, “Refinements of the Hermite–Hadamard inequality for coordinated convex mappings”, Journal of Applied Analysis, vol. 25, no. 1, pp. 73-81, 2019.
  • [5] H. Budak, F. Usta, M. Z. Sarikaya, M. E. Ozdemir, “On generalization of midpoint type inequalities with generalized fractional integral operators”, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, vol. 113, no. 2, pp. 769-790, 2019.
  • [6] H. Budak, F. Usta, “New Upper Bounds of Ostrowski Type Integral Inequalities Utilizing Taylor Expansion”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 3, pp. 567-578, 2018.
  • [7] S. S. Dragomir, C. E. M. Pearce, "Selected Topics on Hermite-Hadamard Inequalities and Applications", RGMIA Monographs, Victoria University, 2000.
  • [8] S. S. Dragomir, J. Pecaric, L. E. Persson, "Some inequalities of Hadamard Type", Soochow Journal of Mathematics, vol. 21, no. 3, pp. 335–341, 2001.
  • [9] S. S. Dragomir, Th. M. Rassias, "Ostrowski type inequalities and applications in numerical integration", Kluwer Academic Publishers, Dorcdrecht, Boston, London, 2002.
  • [10] İ. İşcan, New estimates on generalization of some integral inequalities for s-convex functions and their applications, Int. J. Pure Appl. Math., vol. 86, no. 4, pp. 727-746, 2013.
  • [11] H. Kadakal, "Hermite–Hadamard type inequalities for trigonometrically convex functions", Scientific Studies and Research. Series Mathematics and Informatics, vol. 28, no. 2, pp. 19–28, 2018.
  • [12] M. Kadakal, İ. İşcan, Inequalities of Hermite-Hadamard and Bullen Type for AH -Convex Functions. Universal Journal of Mathematics and Applications, vol. 2, no. 3, pp. 152-158, 2019.
  • [13] M. Kadakal, “Better Results for Trigonometrically Convex Functions via Hölder-İşcan and Improved Power-Mean Inequalities”, Universal Journal of Mathematics and Applications, vol. 3, no. 1, pp. 38-43, 2020.
  • [14] M. Z. Sarikaya, E. Set, M. E. Özdemir, "On new inequalities of Simpson’s type for convex functions", Computers & Mathematics with Applications, vol. 60, no. 8, pp. 2191-2199, 2010.
  • [15] M. Z. Sarikaya, N. Aktan, "On the generalization of some integral inequalities and their applications", Mathematical and Computer Modelling, vol. 54, no. 9-10, pp. 2175-2182, 2011.
  • [16] F. Usta, M. Z. Sarıkaya, “Explicit Bounds on Certain Integral Inequalities via Conformable Fractional Calculus, Cogent Mathematics, vol. 4, no. 1, 1277505, 2017.
  • [17] F. Usta, “On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators”, Filomat, vol. 32, no. 6, 2018.
  • [18] F. Usta, M. Z. Sarıkaya, “On Generalization of Pachpatte Type Inequalities for Conformable Fractional Integral, TWMS Journal of Applied and Engineering Mathematics, vol. 8, no. 1, 106, 2018.
  • [19] F. Usta, M. Z. Sarıkaya, “On Bivariate Retarded Integral Inequalities and Their Applications” Facta Universitatis, Series: Mathematics and Informatics, vol. 34, no. 3, pp. 553-561, 2019.
  • [20] F. Usta, H. Budak, M. Z. Sarıkaya, “Montgomery Identities and Ostrowski type Inequalities for Fractional Integral Operators”, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, vol. 113, no. 2, pp. 1059-1080, 2019.
  • [21] F. Usta, H. Budak, F. Ertuğral, M. Z. Sarıkaya, “The Minkowski’s Inequalities Utilizing Newly Defined Generalized Fractional Integral Operators, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, pp. 686-701, 2019.
  • [22] F. Usta, H. Budak, M. Z. Sarıkaya, “Some New Chebyshev Type Inequalities Utilizing Generalized Fractional Integral Opetors”, AIMS Mathematics, vol. 5, no. 2, 2020.
  • [23] S. Varošanec, "On h-convexity", J. Math. Anal. Appl., vol. 326, no. 1, pp. 303–311, 2007.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Sercan Turhan 0000-0002-4392-2182

Publication Date August 1, 2020
Submission Date March 30, 2020
Acceptance Date May 10, 2020
Published in Issue Year 2020 Volume: 24 Issue: 4

Cite

APA Turhan, S. (2020). Novel Results based on Generalisation of Some Integral Inequalities for Trigonometrically -P Function. Sakarya University Journal of Science, 24(4), 665-674. https://doi.org/10.16984/saufenbilder.711507
AMA Turhan S. Novel Results based on Generalisation of Some Integral Inequalities for Trigonometrically -P Function. SAUJS. August 2020;24(4):665-674. doi:10.16984/saufenbilder.711507
Chicago Turhan, Sercan. “Novel Results Based on Generalisation of Some Integral Inequalities for Trigonometrically -P Function”. Sakarya University Journal of Science 24, no. 4 (August 2020): 665-74. https://doi.org/10.16984/saufenbilder.711507.
EndNote Turhan S (August 1, 2020) Novel Results based on Generalisation of Some Integral Inequalities for Trigonometrically -P Function. Sakarya University Journal of Science 24 4 665–674.
IEEE S. Turhan, “Novel Results based on Generalisation of Some Integral Inequalities for Trigonometrically -P Function”, SAUJS, vol. 24, no. 4, pp. 665–674, 2020, doi: 10.16984/saufenbilder.711507.
ISNAD Turhan, Sercan. “Novel Results Based on Generalisation of Some Integral Inequalities for Trigonometrically -P Function”. Sakarya University Journal of Science 24/4 (August 2020), 665-674. https://doi.org/10.16984/saufenbilder.711507.
JAMA Turhan S. Novel Results based on Generalisation of Some Integral Inequalities for Trigonometrically -P Function. SAUJS. 2020;24:665–674.
MLA Turhan, Sercan. “Novel Results Based on Generalisation of Some Integral Inequalities for Trigonometrically -P Function”. Sakarya University Journal of Science, vol. 24, no. 4, 2020, pp. 665-74, doi:10.16984/saufenbilder.711507.
Vancouver Turhan S. Novel Results based on Generalisation of Some Integral Inequalities for Trigonometrically -P Function. SAUJS. 2020;24(4):665-74.