<i>p</i>-Convex Functions and Some of Their Properties

Sezer, Sevda; Eken, Zeynep; Tınaztepe, Gültekin; Adi̇lov, Gabil

doi:10.1080/01630563.2021.1884876

Cited by 29 publications

(14 citation statements)

References 15 publications

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“…In the future, more interesting inequalities regarding special functions can be obtained through different examples of p-convex functions. The introduction of p-convex functions and their properties for n dimensional case are given in [22]. By making use of that study, the existence of similar results can be investigated for multiple integrals.…”

Section: Discussionmentioning

confidence: 99%

“…Some of the studies on p-convex sets and their properties can be seen in [17] - [21]. p-convex functions are shortly introduced in [17] and its main characteristics are given in [22]. Definition 1.1.…”

Section: Introductionmentioning

confidence: 99%

“…It is clear that any interval of real numbers including zero or accepting zero as a boundary point is a p-convex set. Using Theorem 3.2 in [22], we can give the following definition of p-convex function: Definition 1.2. Let U ⊆ R a p-convex set and let f : U → R be a function.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex

Barut¹

2021

Fundamental Journal of Mathematics and Applications

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In this paper, we extend some estimates of a Hermite-Hadamard type inequality for functions whose absolute values of the first derivatives are p-convex. By means of the obtained inequalities, some bound functions involving beta functions and hypergeometric functions are derived as applications. Also, we suggest an upper bound for error in numerical integration of p-convex functions via composite trapezoid rule.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex

Barut¹

2021

Fundamental Journal of Mathematics and Applications

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“…The classical definition of convex functions was given in [3]. Another concept which is used widely in convex analysis is p-convex sets and p-convexity (see [4]). By taking p = 1 in the above definition, we get classical notion of convexity.…”

Section: Introductionmentioning

confidence: 99%

Fractional Versions of Hermite-Hadamard, Fejér, and Schur Type Inequalities for Strongly Nonconvex Functions

Muhammad

Yasin

et al. 2022

Journal of Function Spaces

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In modern world, most of the optimization problems are nonconvex which are neither convex nor concave. The objective of this research is to study a class of nonconvex functions, namely, strongly nonconvex functions. We establish inequalities of Hermite-Hadamard and Fejér type for strongly nonconvex functions in generalized sense. Moreover, we establish some fractional integral inequalities for strongly nonconvex functions in generalized sense in the setting of Riemann-Liouville integral operators.

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“…The theoretical and applied developments leads to the new kind of convexities such as B−convexity, B −1 −convexity, p−convexity etc [2,5,15,19]. Many types of inequalities obtained for classical convex functions are studied and extended for new convexity types.…”

Section: Introductionmentioning

confidence: 99%