Inequalities for interval-valued Riemann diamond-alpha integrals

Abstract We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals....
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Autor*in:	Bohner, Martin [verfasserIn] Nguyen, Linh Schneider, Baruch Truong, Tri

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Interval-valued functions Time scales Diamond-alpha integral Jensen’s inequalities Hölder’s inequalities Minkowski’s inequalities

Anmerkung:	© The Author(s) 2023

Übergeordnetes Werk:	Enthalten in: Journal of inequalities and applications - Heidelberg : Springer, 2005, 2023(2023), 1 vom: 19. Juni
Übergeordnetes Werk:	volume:2023 ; year:2023 ; number:1 ; day:19 ; month:06

Links:	Volltext

DOI / URN:	10.1186/s13660-023-02993-3

Katalog-ID:	SPR051954036

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520			\|a Abstract We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals. With the help of the interval Riemann diamond-alpha integral, we present interval variants of Jensen inequalities for convex and concave interval-valued functions on an arbitrary time scale. Moreover, diamond-alpha Hölder’s and Minkowski’s interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results.
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allfields	10.1186/s13660-023-02993-3 doi (DE-627)SPR051954036 (SPR)s13660-023-02993-3-e DE-627 ger DE-627 rakwb eng Bohner, Martin verfasserin aut Inequalities for interval-valued Riemann diamond-alpha integrals 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals. With the help of the interval Riemann diamond-alpha integral, we present interval variants of Jensen inequalities for convex and concave interval-valued functions on an arbitrary time scale. Moreover, diamond-alpha Hölder’s and Minkowski’s interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results. Interval-valued functions (dpeaa)DE-He213 Time scales (dpeaa)DE-He213 Diamond-alpha integral (dpeaa)DE-He213 Jensen’s inequalities (dpeaa)DE-He213 Hölder’s inequalities (dpeaa)DE-He213 Minkowski’s inequalities (dpeaa)DE-He213 Nguyen, Linh aut Schneider, Baruch aut Truong, Tri aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2023(2023), 1 vom: 19. Juni (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2023 year:2023 number:1 day:19 month:06 https://dx.doi.org/10.1186/s13660-023-02993-3 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2023 2023 1 19 06
spelling	10.1186/s13660-023-02993-3 doi (DE-627)SPR051954036 (SPR)s13660-023-02993-3-e DE-627 ger DE-627 rakwb eng Bohner, Martin verfasserin aut Inequalities for interval-valued Riemann diamond-alpha integrals 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals. With the help of the interval Riemann diamond-alpha integral, we present interval variants of Jensen inequalities for convex and concave interval-valued functions on an arbitrary time scale. Moreover, diamond-alpha Hölder’s and Minkowski’s interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results. Interval-valued functions (dpeaa)DE-He213 Time scales (dpeaa)DE-He213 Diamond-alpha integral (dpeaa)DE-He213 Jensen’s inequalities (dpeaa)DE-He213 Hölder’s inequalities (dpeaa)DE-He213 Minkowski’s inequalities (dpeaa)DE-He213 Nguyen, Linh aut Schneider, Baruch aut Truong, Tri aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2023(2023), 1 vom: 19. Juni (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2023 year:2023 number:1 day:19 month:06 https://dx.doi.org/10.1186/s13660-023-02993-3 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2023 2023 1 19 06
allfields_unstemmed	10.1186/s13660-023-02993-3 doi (DE-627)SPR051954036 (SPR)s13660-023-02993-3-e DE-627 ger DE-627 rakwb eng Bohner, Martin verfasserin aut Inequalities for interval-valued Riemann diamond-alpha integrals 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals. With the help of the interval Riemann diamond-alpha integral, we present interval variants of Jensen inequalities for convex and concave interval-valued functions on an arbitrary time scale. Moreover, diamond-alpha Hölder’s and Minkowski’s interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results. Interval-valued functions (dpeaa)DE-He213 Time scales (dpeaa)DE-He213 Diamond-alpha integral (dpeaa)DE-He213 Jensen’s inequalities (dpeaa)DE-He213 Hölder’s inequalities (dpeaa)DE-He213 Minkowski’s inequalities (dpeaa)DE-He213 Nguyen, Linh aut Schneider, Baruch aut Truong, Tri aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2023(2023), 1 vom: 19. Juni (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2023 year:2023 number:1 day:19 month:06 https://dx.doi.org/10.1186/s13660-023-02993-3 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2023 2023 1 19 06
allfieldsGer	10.1186/s13660-023-02993-3 doi (DE-627)SPR051954036 (SPR)s13660-023-02993-3-e DE-627 ger DE-627 rakwb eng Bohner, Martin verfasserin aut Inequalities for interval-valued Riemann diamond-alpha integrals 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals. With the help of the interval Riemann diamond-alpha integral, we present interval variants of Jensen inequalities for convex and concave interval-valued functions on an arbitrary time scale. Moreover, diamond-alpha Hölder’s and Minkowski’s interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results. Interval-valued functions (dpeaa)DE-He213 Time scales (dpeaa)DE-He213 Diamond-alpha integral (dpeaa)DE-He213 Jensen’s inequalities (dpeaa)DE-He213 Hölder’s inequalities (dpeaa)DE-He213 Minkowski’s inequalities (dpeaa)DE-He213 Nguyen, Linh aut Schneider, Baruch aut Truong, Tri aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2023(2023), 1 vom: 19. Juni (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2023 year:2023 number:1 day:19 month:06 https://dx.doi.org/10.1186/s13660-023-02993-3 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2023 2023 1 19 06
allfieldsSound	10.1186/s13660-023-02993-3 doi (DE-627)SPR051954036 (SPR)s13660-023-02993-3-e DE-627 ger DE-627 rakwb eng Bohner, Martin verfasserin aut Inequalities for interval-valued Riemann diamond-alpha integrals 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals. With the help of the interval Riemann diamond-alpha integral, we present interval variants of Jensen inequalities for convex and concave interval-valued functions on an arbitrary time scale. Moreover, diamond-alpha Hölder’s and Minkowski’s interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results. Interval-valued functions (dpeaa)DE-He213 Time scales (dpeaa)DE-He213 Diamond-alpha integral (dpeaa)DE-He213 Jensen’s inequalities (dpeaa)DE-He213 Hölder’s inequalities (dpeaa)DE-He213 Minkowski’s inequalities (dpeaa)DE-He213 Nguyen, Linh aut Schneider, Baruch aut Truong, Tri aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2023(2023), 1 vom: 19. Juni (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2023 year:2023 number:1 day:19 month:06 https://dx.doi.org/10.1186/s13660-023-02993-3 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2023 2023 1 19 06
language	English
source	Enthalten in Journal of inequalities and applications 2023(2023), 1 vom: 19. Juni volume:2023 year:2023 number:1 day:19 month:06
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topic_facet	Interval-valued functions Time scales Diamond-alpha integral Jensen’s inequalities Hölder’s inequalities Minkowski’s inequalities
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author	Bohner, Martin
spellingShingle	Bohner, Martin misc Interval-valued functions misc Time scales misc Diamond-alpha integral misc Jensen’s inequalities misc Hölder’s inequalities misc Minkowski’s inequalities Inequalities for interval-valued Riemann diamond-alpha integrals
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topic_title	Inequalities for interval-valued Riemann diamond-alpha integrals Interval-valued functions (dpeaa)DE-He213 Time scales (dpeaa)DE-He213 Diamond-alpha integral (dpeaa)DE-He213 Jensen’s inequalities (dpeaa)DE-He213 Hölder’s inequalities (dpeaa)DE-He213 Minkowski’s inequalities (dpeaa)DE-He213
topic	misc Interval-valued functions misc Time scales misc Diamond-alpha integral misc Jensen’s inequalities misc Hölder’s inequalities misc Minkowski’s inequalities
topic_unstemmed	misc Interval-valued functions misc Time scales misc Diamond-alpha integral misc Jensen’s inequalities misc Hölder’s inequalities misc Minkowski’s inequalities
topic_browse	misc Interval-valued functions misc Time scales misc Diamond-alpha integral misc Jensen’s inequalities misc Hölder’s inequalities misc Minkowski’s inequalities
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title	Inequalities for interval-valued Riemann diamond-alpha integrals
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title_full	Inequalities for interval-valued Riemann diamond-alpha integrals
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title_sort	inequalities for interval-valued riemann diamond-alpha integrals
title_auth	Inequalities for interval-valued Riemann diamond-alpha integrals
abstract	Abstract We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals. With the help of the interval Riemann diamond-alpha integral, we present interval variants of Jensen inequalities for convex and concave interval-valued functions on an arbitrary time scale. Moreover, diamond-alpha Hölder’s and Minkowski’s interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results. © The Author(s) 2023
abstractGer	Abstract We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals. With the help of the interval Riemann diamond-alpha integral, we present interval variants of Jensen inequalities for convex and concave interval-valued functions on an arbitrary time scale. Moreover, diamond-alpha Hölder’s and Minkowski’s interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results. © The Author(s) 2023
abstract_unstemmed	Abstract We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals. With the help of the interval Riemann diamond-alpha integral, we present interval variants of Jensen inequalities for convex and concave interval-valued functions on an arbitrary time scale. Moreover, diamond-alpha Hölder’s and Minkowski’s interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results. © The Author(s) 2023
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title_short	Inequalities for interval-valued Riemann diamond-alpha integrals
url	https://dx.doi.org/10.1186/s13660-023-02993-3
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up_date	2024-07-04T00:36:10.442Z
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score	7.400141

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Inequalities for interval-valued Riemann diamond-alpha integrals

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