New integral representations of nth order convex functions

Rajba, Teresa

doi:10.1016/j.jmaa.2011.01.055

Cited by 8 publications

(4 citation statements)

References 19 publications

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“…, n is positive; see Ref. [89] and references therein for details. In our case the function h(x) is given by the exponential e z which is an n-convex function for any n ∈ N as d (n) e z /dz n = e z > 0.…”

Section: Geometrical Interpretationmentioning

confidence: 99%

Generalized ghost-free propagators in nonlocal field theories

et al. 2020

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In this paper we present an iterative method to generate an infinite class of new nonlocal field theories whose propagators are ghost-free. We first examine the scalar field case and show that the pole structure of such generalized propagators possesses the standard two derivative pole and in addition can contain complex conjugate poles which, however, do not spoil at least tree level unitarity as the optical theorem is still satisfied. Subsequently, we define analogous propagators for the fermionic sector which is also devoid of unhealthy degrees of freedom. As a third case, we apply the same construction to gravity and define a new set of theories whose graviton propagators around the Minkowski background are ghost-free. Such a wider class also includes nonlocal theories previously studied, and Einstein's general relativity as a peculiar limit. Moreover, we compute the linearized gravitational potential generated by a static point-like source for several gravitational theories belonging to this new class and show that the nonlocal nature of gravity regularizes the singularity at the origin.

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Section: Geometrical Interpretationmentioning

confidence: 99%

Generalized ghost-free propagators in nonlocal field theories

et al. 2020

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“…The inequality (2.25) coincides with (2.23) for the spline function f (x) = (x − t) s + . Moreover, it is well known that s-convex function has the integral representation, such that the spline functions are the generating functions (see [18] Remark 2.11. Necessary and sufficient conditions for the verification of the (s+1)-convex order, which are given in Proposition 2.8, can be difficult to checking.…”

Section: )mentioning

confidence: 99%

Section: Proposition 28 ([8]mentioning

confidence: 99%

On a generalization of a theorem of Levin and Stečkin and inequalities of the Hermite-Hadamard type

Rajba¹

2017

Mathematical Inequalities &Amp; Applications

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“…These results are applied to derive some inequalities between quadrature operators. We define also and study strong delta-convexity of n -th order that generalizes strong n -convexity studied in [14] and [9].…”

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confidence: 99%

On strong delta-convexity and Hermite-Hadamard type inequalities for delta-convex functions of higher order

Rajba¹

2015

Mathematical Inequalities &Amp; Applications

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Abstract. In our previous paper [15], using s -convex stochastic ordering [4], we investigate Hermite-Hadamard-Fejér type inequalities in the case of higher order convex functions. In the present paper, our aim is to extend this investigation from convex to delta-convex functions of higher order [8]. We offer some useful tools for obtaining and proving of various forms of the Hermite-Hadamard-Fejér type inequalities for delta-convex functions of higher order, that generalizes results of Dragomir et al. [5]. These results are applied to derive some inequalities between quadrature operators. We define also and study strong delta-convexity of n -th order that generalizes strong n -convexity studied in [14] and [9].Mathematics subject classification (2010): 26A51, 39B62.

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New integral representations of nth order convex functions

Cited by 8 publications

References 19 publications

Generalized ghost-free propagators in nonlocal field theories

Generalized ghost-free propagators in nonlocal field theories

On a generalization of a theorem of Levin and Stečkin and inequalities of the Hermite-Hadamard type

On strong delta-convexity and Hermite-Hadamard type inequalities for delta-convex functions of higher order

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