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Title |
SVN-Ostrowski Type Inequalities for (Alpha, Beta, Gammar, Delta)-Convex Functions |
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Author |
Maria Khan, Asif Raza Khan, Ali Hassan |
| Citation |
Vol. 24 No. 1 pp. 85-94 |
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Abstract |
In this paper, we present the very first time the generalized notion of (Alpha, Beta, Gammar, Delta)- convex (concave) function in mixed kind, which is the generalization of (Alpha, Beta)-convex (concave) functions in 1st and 2nd kind, (s,r)-convex (concave) functions in mixed kind, s-convex (concave) functions in 1st and 2nd kind, P-convex (concave) functions, quasi convex(concave) functions and the class of convex (concave) functions. We would like to state the well-known Ostrowski inequality via SVN-Riemann Integrals for (Alpha, Beta, Gammar, Delta)- convex (concave) function in mixed kind. Moreover we establish some SVN-Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are (Alpha, Beta, Gammar, Delta)-convex (concave) functions in mixed kind by using different techniques including Holders inequality and power mean inequality. Also, various established results would be captured as special cases with respect to convexity of function. |
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Keywords |
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Title |
SVN-Ostrowski Type Inequalities for (A, B, G, D)-Convex Functions |
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Author |
Maria Khan, Asif Raza Khan, Ali Hassan |
| Citation |
Vol. 24 No. 1 pp. 85-94 |
|
Abstract |
In this paper, we present the very first time the generalized notion of (A, B, G, D)- convex (concave) function in mixed kind, which is the generalization of (A, B)-convex (concave) functions in 1st and 2nd kind, (s, r)-convex (concave) functions in mixed kind, s-convex (concave) functions in 1st and 2nd kind, P-convex (concave) functions, quasi convex(concave) functions and the class of convex (concave) functions. We would like to state the well-known Ostrowski inequality via SVN-Riemann Integrals for (A, B, G, D)- convex (concave) function in mixed kind. Moreover we establish some SVN-Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are (A, B, G, D)-convex (concave) functions in mixed kind by using different techniques including Holders inequality and power mean inequality. Also, various established results would be captured as special cases with respect to convexity of function. |
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Keywords |
Ostrowski inequality, (A, B, G, D)-convex functions, Single valued Neutrosophic sets. |
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