On Harmonically<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>h</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-Preinvex Functions

Wu, Shanhe; Baloch, Imran Abbas; Işcan, İ̇mdat

doi:10.1155/2017/2148529

Cited by 14 publications

(9 citation statements)

References 20 publications

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“…Usually, the preinvex functions can be convexity if ζ(u 2 , u 1 ) = u 2 − u 1 holds in (2). Other properties of preinvex functions are given in [21,22].…”

Section: Definition 4 [20]mentioning

confidence: 99%

Some Integral Inequalities for h-Godunova-Levin Preinvexity

Almutairi

Kılıçman

2019

Symmetry

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In this study, we define new classes of convexity called h-Godunova-Levin and h-Godunova-Levin preinvexity, through which some new inequalities of Hermite-Hadamard type are established. These new classes are the generalization of several known convexities including the s-convex, P-function, and Godunova-Levin. Further, the properties of the h-Godunova-Levin function are also discussed. Meanwhile, the applications of h-Godunova-Levin Preinvex function are given.

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“…Usually, the preinvex functions can be convexity if ζ(u 2 , u 1 ) = u 2 − u 1 holds in (2). Other properties of preinvex functions are given in [21,22].…”

Section: Definition 4 [20]mentioning

confidence: 99%

Some Integral Inequalities for h-Godunova-Levin Preinvexity

Almutairi

Kılıçman

2019

Symmetry

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“…Usually, the preinvex functions can be convexity if ζ(u 2 , u 1 ) = u 2 − u 1 holds in (2). Other properties of preinvex functions are given in [15,16].…”

Section: Definition 4 [19]mentioning

confidence: 99%

Some Integral Inequalities for <em>h</em>-Godunova-Levin Preinvexity

Almutairi¹,

Kılıçman²

2019

Preprint

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In this study, we define new classes of convexity called of h-Godunova-Levin and h-Godunova-Levin preinvexity, through which some new inequalities of Hermite-Hadamard type were established. These new classes are the generalisation of several known convexity including the s-convex, P-function, Godunova-Levin. Further, the properties of h-Godunova-Levin function were also discussed. Meanwhile, the applications of h-Godunova-Levin Preinvex function are given

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“…Many famous inequalities can be obtained using the concept of convex functions. For details, interested readers are referred to [4][5][6][7][8][9][10][11][12][13][14]. Among these inequalities, Hermite-Hadamard's inequality, which provides us a necessary and sufficient condition for a function to be convex, is one of the most studied results.…”

Section: Introductionmentioning

confidence: 99%