NEW NTEGRAL INEQUALITIES FOR s-CONVEX FUNCTION IN THE THIRD SENSE
SERAP KEMALI *
Vocational School of Technical Sciences, Akdeniz University, Antalya, Turkey.
BAKI UNAL
Department of Mathematics, Graduate School of Sciences, Akdeniz University, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, some new integral inequalities are obtained for functions whose n-th derivative is s-convex function in the third sense with the help of an integral identity. Then, by putting special conditions in these integral inequalities, new integral inequalities for classical convex functions are obtained.
Keywords: Convex function, s-convex functions in the third sense, Holder integral inequality, power mean integral inequality
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References
Adilov G, Yesilce _I. On generalizations of the concept of convexity. Hacettepe Journal of Mathematics and Statistics. 2012;41(5):723-730.
Adilov G, Tnaztepe G, Tnaztepe R. On the global minimization of increasing positively homogeneous functions over the unit simplex. International Journal of
Computer Mathematics. 2010;87(12):2733-2746.
Iscan I, Kunt M, Yazici N. Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integrals. New Trends in Mathematical Sciences. 2016;4(3):239.
Iscan I, Kadakal H, Kadakal M. Some new integral inequalities for n-times differentiable log-convex functions. New Trends in Mathematical Sciences. 2017;5(2):10-15.
Iscan I, Kadakal H, Kadakal M. Some new integral inequalities for functions whose nth derivatives in absolute value are (a, m)-convex functions. New Trends in
Mathematical Sciences. 2017;5(2):180-185.
Iscan I, Aydin M. On new general integral inequalities for h-convex function. New Trends in Mathematical Sciences. 2016;4(3):73-87.
Kemali S, Yesilce _I, Adilov G. B-convexity, B?1-convexity, and their comparison, Numerical Functional Analysis and Optimization. 2015;36(2):133-146.
Kemali S, Sezer S, Tnaztepe G, Adilov G. s-Convex functions in the third sense. The Korean Journal of Mathematics. 2021;29(3):593-602.
Sezer S, Eken Z, Tinaztepe G, Adilov G. p-Convex functions and some of theirp properties. Numerical Functional Analysis and Optimization. 2021;42(4):443-459.
Sezer S. The Hermite-Hadamard inequality for s-Convex functions in the third sense. AIMS Mathematics. 2021;6(7):7719-7732.
Orlicz W. A note on modular spaces I, Bull. Acad. Polon. Soi., Ser. Math. Astronom Phys. 1961;9:157-162.
Breckner WW. Stetigkeitsaussagen fiur eine Klasse verallgemekterter konvexer Funktionen in topologischen linearen Raumen. Publ. Inst. Math. 1978;23:13-20.
Eken Z. Hermite-Hadamard Type Inequalities related s-convex functions in the third sense. Turkish Journal of Mathematics and Computer Science. ;13(2).
Chen F, Wu S. Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions. Journal of Nonlinear Science Applications. ;9:705-716.
Available:www.tjnsa.com
Dragomir SS, Pecaric J, Persson LE. Some inequalities of Hadamard type. Soochow J. Math. 1995;21(3):335-341.
Khan MA, Chu Y, Khan TU, Khan J. Some new inequalities of Hermite-Hadamard type for s-convex functions with applications. Open Mathematics. 2017;15(1):1414-1430.
Available:https://doi.org/10.1515/math-2017-0121
Kirmaci U, Bakula M, Ozdemir M, Pecaric J. Hadamard-tpye inequalities for s-convex functions. Appl. Math. Comp. 2007;193:26-35.
Maden S, Kadakal H, Kadakal M, Iscan I. Some new integral inequalities for n-times dierentiable convex and concave functions. Journal of Nonlinear Sciences and Applications. 2017;10(12):6141-6148.
Sarikaya MZ, Kiris ME. Some new inequalities of Hermite-Hadamard type for s-convex functions. Miskolc Mathematical Notes. 2015;16(1):491-501.
Available:https://doi.org/10.18514/MMN.2015.1099.