On the Generalization of Opial Type Inequality for Convex Function

Mehmet Zeki Sarıkaya

Research Article

On the Generalization of Opial Type Inequality for Convex Function

Year 2019, Volume: 7 Issue: 2, 456 - 461, 15.10.2019

Abstract

In this article, by using new different approach method, we establish some generalization of Opial like inequality for convex mappings.

Keywords

Opial inequality , convex function.

References

[1] R.P. Agarwal and P.Y.H. Pang, Opial inequalities with applications in differential and difference equations, Mathematics and Its Applications book series (MAIA, volume 320), Kluwer Academic Publishers, London, 1995.
[2] W.S. Cheung, Some new Opial-type inequalities, Mathematika, 37 (1990), 136–142.
[3] W.S. Cheung, Some generalized Opial-type inequalities, J. Math. Anal. Appl., 162 (1991), 317– 321.
[4] E.K. Godunova and V.l. Levin, On an inequality of Maroni, (Russian), Mat. Zametki 2(1967), 221-224.
[5] X. G. He, A short of a generalization on Opial’ s inequailty,Journal of Mathematical Analysis and Applications,182, (1994), 299-300.
[6] P. Maroni, Sur l’in´egalit´e d’Opial-Beesack, C. R. Acad. Sci. Paris Ser. A-B, 264 (1967), A62–A64.
[7] Hua L.K., On an inequality of Opial, Sci China., 14(1965), 789-790.
[8] C. Olech, A simple proof of a certain result of Z. Opial. Ann. Polon. Math. 8 (1960), 61–63.
[9] Z. Opial, Sur une inegaliti, Ann. Polon. Math. 8 (1960), 29-32.
[10] B. G. Pachpatte, On Opial-type integral inequalities , J. Math. Anal. Appl. 120 (1986), 547–556.
[11] B. G. Pachpatte, Some inequalities similar to Opial’s inequality , Demonstratio Math. 26 (1993), 643–647.
[12] B. G. Pachpatte, A note on some new Opial type integral inequalities, Octogon Math. Mag. 7 (1999), 80–84.
[13] B. G. Pachpatte, On some inequalities of the Weyl type, An. Stiint. Univ. “Al.I. Cuza” Iasi 40 (1994), 89–95.
[14] S.H. Saker, M.D. Abdou and I. Kubiaczyk, Opial and Polya type inequalities via convexity, Fasciculi Mathematici, 60(1), 145–159, 2018.
[15] H. M. Srivastava, K.-L. Tseng, S.-J. Tseng and J.-C. Lo, Some weighted Opial-type inequalities on time scales, Taiwanese J. Math., 14 (2010), 107–122.
[16] C.-J. Zhao and W.-S. Cheung, On Opial-type integral inequalities and applications. Math. Inequal. Appl. 17 (2014), no. 1, 223–232.
[17] F. H. Wong, W. C. Lian, S. L. Yu and C. C. Yeh, Some generalizations of Opial’s inequalities on time scales, Taiwanese Journal of Mathematics, Vol. 12, Number 2, April 2008, Pp. 463–471.

Year 2019, Volume: 7 Issue: 2, 456 - 461, 15.10.2019

Mehmet Zeki Sarıkaya

Abstract

References

[1] R.P. Agarwal and P.Y.H. Pang, Opial inequalities with applications in differential and difference equations, Mathematics and Its Applications book series (MAIA, volume 320), Kluwer Academic Publishers, London, 1995.
[2] W.S. Cheung, Some new Opial-type inequalities, Mathematika, 37 (1990), 136–142.
[3] W.S. Cheung, Some generalized Opial-type inequalities, J. Math. Anal. Appl., 162 (1991), 317– 321.
[4] E.K. Godunova and V.l. Levin, On an inequality of Maroni, (Russian), Mat. Zametki 2(1967), 221-224.
[5] X. G. He, A short of a generalization on Opial’ s inequailty,Journal of Mathematical Analysis and Applications,182, (1994), 299-300.
[6] P. Maroni, Sur l’in´egalit´e d’Opial-Beesack, C. R. Acad. Sci. Paris Ser. A-B, 264 (1967), A62–A64.
[7] Hua L.K., On an inequality of Opial, Sci China., 14(1965), 789-790.
[8] C. Olech, A simple proof of a certain result of Z. Opial. Ann. Polon. Math. 8 (1960), 61–63.
[9] Z. Opial, Sur une inegaliti, Ann. Polon. Math. 8 (1960), 29-32.
[10] B. G. Pachpatte, On Opial-type integral inequalities , J. Math. Anal. Appl. 120 (1986), 547–556.
[11] B. G. Pachpatte, Some inequalities similar to Opial’s inequality , Demonstratio Math. 26 (1993), 643–647.
[12] B. G. Pachpatte, A note on some new Opial type integral inequalities, Octogon Math. Mag. 7 (1999), 80–84.
[13] B. G. Pachpatte, On some inequalities of the Weyl type, An. Stiint. Univ. “Al.I. Cuza” Iasi 40 (1994), 89–95.
[14] S.H. Saker, M.D. Abdou and I. Kubiaczyk, Opial and Polya type inequalities via convexity, Fasciculi Mathematici, 60(1), 145–159, 2018.
[15] H. M. Srivastava, K.-L. Tseng, S.-J. Tseng and J.-C. Lo, Some weighted Opial-type inequalities on time scales, Taiwanese J. Math., 14 (2010), 107–122.
[16] C.-J. Zhao and W.-S. Cheung, On Opial-type integral inequalities and applications. Math. Inequal. Appl. 17 (2014), no. 1, 223–232.
[17] F. H. Wong, W. C. Lian, S. L. Yu and C. C. Yeh, Some generalizations of Opial’s inequalities on time scales, Taiwanese Journal of Mathematics, Vol. 12, Number 2, April 2008, Pp. 463–471.

There are 17 citations in total.

Details

Primary Language	English
Subjects	Engineering
Journal Section	Research Article
Authors	Mehmet Zeki Sarıkaya 0000-0002-6165-9242
Submission Date	July 31, 2019
Acceptance Date	September 30, 2019
Publication Date	October 15, 2019
Published in Issue	Year 2019 Volume: 7 Issue: 2

Cite

APA	Sarıkaya, M. Z. (2019). On the Generalization of Opial Type Inequality for Convex Function. Konuralp Journal of Mathematics, 7(2), 456-461.
AMA	Sarıkaya MZ. On the Generalization of Opial Type Inequality for Convex Function. Konuralp J. Math. October 2019;7(2):456-461.
Chicago	Sarıkaya, Mehmet Zeki. “On the Generalization of Opial Type Inequality for Convex Function”. Konuralp Journal of Mathematics 7, no. 2 (October 2019): 456-61.
EndNote	Sarıkaya MZ (October 1, 2019) On the Generalization of Opial Type Inequality for Convex Function. Konuralp Journal of Mathematics 7 2 456–461.
IEEE	M. Z. Sarıkaya, “On the Generalization of Opial Type Inequality for Convex Function”, Konuralp J. Math., vol. 7, no. 2, pp. 456–461, 2019.
ISNAD	Sarıkaya, Mehmet Zeki. “On the Generalization of Opial Type Inequality for Convex Function”. Konuralp Journal of Mathematics 7/2 (October2019), 456-461.
JAMA	Sarıkaya MZ. On the Generalization of Opial Type Inequality for Convex Function. Konuralp J. Math. 2019;7:456–461.
MLA	Sarıkaya, Mehmet Zeki. “On the Generalization of Opial Type Inequality for Convex Function”. Konuralp Journal of Mathematics, vol. 7, no. 2, 2019, pp. 456-61.
Vancouver	Sarıkaya MZ. On the Generalization of Opial Type Inequality for Convex Function. Konuralp J. Math. 2019;7(2):456-61.