Extensions of certain integral inequalities on time scales

Özkan, Umut Mutlu; Sarıkaya, Mehmet Zeki; Yıldırım, Hüseyin

doi:10.1016/j.aml.2007.06.008

Cited by 68 publications

(37 citation statements)

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“…Since then, many authors have studied certain integral inequalities or dynamic equations on time scales [1,7,8,16,[28][29][30][31]36]. In [8], Bohner and Matthews established the following so-called Ostrowski inequality on time scales which was later generalized by the present authors [18][19][20]23].…”

Section: Introductionmentioning

confidence: 97%

Ostrowski Type Inequalities on Time Scales for Double Integrals

2009

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Section: Introductionmentioning

confidence: 97%

Ostrowski Type Inequalities on Time Scales for Double Integrals

2009

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“…For instance, integral inequalities play a role in the development of a time scales calculus [24]. For more information on classical inequalities, we refer the reader to the recent monograph [9].…”

Section: Introductionmentioning

confidence: 99%

An inequality related to Minkowski type for Sugeno integrals

Ouyang

Mesiar

Agahi

2010

Information Sciences

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“…In particular, when we think of an integral operator as a predictive tool then an integral inequality can be very important in measuring and dimensioning such process. Applications of Minkowski's and Hölder's inequalities have been studied by many authors, for exampleÖzkan et al [22] applied Minkowski's and Hölder's inequalities on time scales and Lu et al [14] used Minkowski's inequality for fast full search in motion estimation.…”

Section: Introductionmentioning

confidence: 99%

On Non-additive Probabilistic Inequalities of Hölder-type

et al. 2011

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Non-additive measure is a generalization of additive probability measure. Integral inequalities play important roles in classical probability and measure theory. Some well-known inequalities such as the Minkowski inequality and the Hölder inequality play important roles not only in the theoretical area but also in application. Non-additive integrals are useful tools in several theoretical and applied statistics which have been built on non-additive measure. For instance, in decision theory and applied statistics, the use of the non-additive integrals can be envisaged from two points of view: decision under uncertainty and multi-criteria decision-making. In fact, the non-additive integrals provide useful tools in many problems in engineering and social choice where the aggregation of data is required. In this paper, Hölder and Minkowski type inequalities for semi(co)normed non-additive integrals are discussed. The main results of this paper generalize some previous results obtained by the authors. Mathematics Subject Classification (2000). Primary 99Z99; Secondary 00A00.

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Extensions of certain integral inequalities on time scales

Abstract: In this work, we establish Hölder's inequality, Minkowski's inequality and Jensen's inequality on time scales via the nabla integral and diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals.

Cited by 68 publications

References 4 publications

Ostrowski Type Inequalities on Time Scales for Double Integrals

Ostrowski Type Inequalities on Time Scales for Double Integrals

An inequality related to Minkowski type for Sugeno integrals

On Non-additive Probabilistic Inequalities of Hölder-type

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