Ostrowski type inequalities via \(\psi-(\alpha,\beta,\gamma,\delta)-\)convex function

Ali Hassan, Asif R. Khan

Abstract


In this paper, we are introducing very first time the class of convex function in mixed kind, which is the generalization of many classes of convex functions. We would like to state well-known Ostrowski inequality via Montgomery identity for convex function in mixed kind. In addition, we establish some Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are -convex functions in mixed kind by using different techniques including Hölder’s inequality and power mean inequality. Also, various established results would be captured as special cases. Moreover, some applications in terms of special means would also be given.


Full Text:

PDF

References


Alomari, M., Darus, M., Dragomir, S.S., Cerone, P.,

Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense,

Appl. Math. Lett., textbf{23}(2010), no. 9, 1071--1076.

Arshad, A., Khan, A.R., Hermite-Hadamard-Fejer type integral inequality for $s-p-$convex of several kinds, Transylvanian J. Math. Mech., textbf{11}(2019), no. 2, 25--40.

Beckenbach, E.F., Bing, R.H., On generalized convex functions,

Trans. Am. Math. Soc., textbf{58}(1945), no. 2, 220--230.

Breckner, W.W., Stetigkeitsaussagen fur eine klasse verallgemeinerter konvexer funktionen in topologischen linearen raumen, Publ. Inst. Math. Univ. German., textbf{23}(1978), no. 37, 13--20.

Dragomir, S.S., On the Ostrowski's integral inequality for mappings with bounded variation and applications, Math. Inequal. Appl., textbf{4}(2001), no. 1, 59--66.

Dragomir, S.S., Refinements of the generalised trapozoid and Ostrowski inequalities for functions of bounded variation, Arch. Math., textbf{91}(2008), no. 5, 450--460.

Dragomir, S.S., A companion of Ostrowski's inequality for functions of bounded variation and applications, Int. J. Nonlinear Anal. Appl., textbf{5}(2014), no. 1, 89--97.

Dragomir, S.S., The functional generalization of Ostrowski inequality via montgomery identity, Acta. Math. Univ. Comenianae, textbf{84}(2015), no. 1, 63--78.

Dragomir, S.S., Barnett, N.S., An Ostrowski type inequality for mappings whose second derivatives are bounded and applications,

J. Indian Math. Soc., textbf{1}(1999), no. 2, 237--245.

Dragomir, S.S., Cerone, P., Barnett, N.S., Roumeliotis, J.,

An inequality of the Ostrowski type for double integrals and applications for cubature formulae, Tamsui. Oxf. J. Inf. Math. Sci., textbf{2}(2000), no. 6, 1--16.

Dragomir, S.S., Cerone, P., Roumeliotis, J., A new generalization of Ostrowski integral inequality for mappings whose derivatives are bounded

and applications in numerical integration and for special means,

Appl. Math. Lett., textbf{13}(2000), no. 1, 19--25.

Hassan, A., Khan, A.R., Generalized fractional Ostrowski type inequalities via $(alpha ,beta ,gamma ,delta )$-convex functions,

Fractional Differential Calculus, {bf 12}(2022), no. 1, 13-26.

Mubeen, S., Habibullah, G.M., K-Fractional integrals and application,

Int. J. Contemp. Math. Sci., textbf{7}(2012), no. 1, 89--94.

Noor, M.A., Awan, M.U., Some integral inequalities for two kinds of convexities via fractional integrals, Trans. J. Math. Mech., textbf{5}(2013), no. 2, 129--136.

Ostrowski, A., "Uber die absolutabweichung einer differentiierbaren Funktion von ihrem integralmittelwert, Comment. Math. Helv., textbf{10}(1937), no. 1, 226--227.

Set, E., New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals,

Comput. Math. Appl., textbf{63}(2012), no. 7, 1147--1154.




DOI: http://dx.doi.org/10.24193/subbmath.2024.2.01

Refbacks

  • There are currently no refbacks.