New Diamond-<i<α</i< Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces

In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula&l...
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Autor*in:	Ksenija Smoljak Kalamir [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	time scales diamond-α integral measure spaces Steffensen-type inequality convex function

Übergeordnetes Werk:	In: Axioms - MDPI AG, 2012, 11(2022), 7, p 323
Übergeordnetes Werk:	volume:11 ; year:2022 ; number:7, p 323

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/axioms11070323

Katalog-ID:	DOAJ028499018

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allfields	10.3390/axioms11070323 doi (DE-627)DOAJ028499018 (DE-599)DOAJ0455f9e1cc9b4a3c8d5e7d8a2c673dfa DE-627 ger DE-627 rakwb eng QA1-939 Ksenija Smoljak Kalamir verfasserin aut New Diamond-<i<α</i< Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula<-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<σ</mi<</semantics<</math<</inline-formula<-finite measures in time scale calculus. Moreover, as a special case, we obtain these inequalities for the delta and the nabla integral. By using the relation between calculus on time scales <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<T</mi<</semantics<</math<</inline-formula< and differential calculus on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<R</mi<</semantics<</math<</inline-formula<, we obtain already-known Steffensen-type inequalities. time scales diamond-α integral measure spaces Steffensen-type inequality convex function Mathematics In Axioms MDPI AG, 2012 11(2022), 7, p 323 (DE-627)718622030 (DE-600)2661511-3 20751680 nnns volume:11 year:2022 number:7, p 323 https://doi.org/10.3390/axioms11070323 kostenfrei https://doaj.org/article/0455f9e1cc9b4a3c8d5e7d8a2c673dfa kostenfrei https://www.mdpi.com/2075-1680/11/7/323 kostenfrei https://doaj.org/toc/2075-1680 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 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_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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 11 2022 7, p 323
spelling	10.3390/axioms11070323 doi (DE-627)DOAJ028499018 (DE-599)DOAJ0455f9e1cc9b4a3c8d5e7d8a2c673dfa DE-627 ger DE-627 rakwb eng QA1-939 Ksenija Smoljak Kalamir verfasserin aut New Diamond-<i<α</i< Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula<-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<σ</mi<</semantics<</math<</inline-formula<-finite measures in time scale calculus. Moreover, as a special case, we obtain these inequalities for the delta and the nabla integral. By using the relation between calculus on time scales <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<T</mi<</semantics<</math<</inline-formula< and differential calculus on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<R</mi<</semantics<</math<</inline-formula<, we obtain already-known Steffensen-type inequalities. time scales diamond-α integral measure spaces Steffensen-type inequality convex function Mathematics In Axioms MDPI AG, 2012 11(2022), 7, p 323 (DE-627)718622030 (DE-600)2661511-3 20751680 nnns volume:11 year:2022 number:7, p 323 https://doi.org/10.3390/axioms11070323 kostenfrei https://doaj.org/article/0455f9e1cc9b4a3c8d5e7d8a2c673dfa kostenfrei https://www.mdpi.com/2075-1680/11/7/323 kostenfrei https://doaj.org/toc/2075-1680 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 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_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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 11 2022 7, p 323
allfields_unstemmed	10.3390/axioms11070323 doi (DE-627)DOAJ028499018 (DE-599)DOAJ0455f9e1cc9b4a3c8d5e7d8a2c673dfa DE-627 ger DE-627 rakwb eng QA1-939 Ksenija Smoljak Kalamir verfasserin aut New Diamond-<i<α</i< Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula<-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<σ</mi<</semantics<</math<</inline-formula<-finite measures in time scale calculus. Moreover, as a special case, we obtain these inequalities for the delta and the nabla integral. By using the relation between calculus on time scales <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<T</mi<</semantics<</math<</inline-formula< and differential calculus on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<R</mi<</semantics<</math<</inline-formula<, we obtain already-known Steffensen-type inequalities. time scales diamond-α integral measure spaces Steffensen-type inequality convex function Mathematics In Axioms MDPI AG, 2012 11(2022), 7, p 323 (DE-627)718622030 (DE-600)2661511-3 20751680 nnns volume:11 year:2022 number:7, p 323 https://doi.org/10.3390/axioms11070323 kostenfrei https://doaj.org/article/0455f9e1cc9b4a3c8d5e7d8a2c673dfa kostenfrei https://www.mdpi.com/2075-1680/11/7/323 kostenfrei https://doaj.org/toc/2075-1680 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 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_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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 11 2022 7, p 323
allfieldsGer	10.3390/axioms11070323 doi (DE-627)DOAJ028499018 (DE-599)DOAJ0455f9e1cc9b4a3c8d5e7d8a2c673dfa DE-627 ger DE-627 rakwb eng QA1-939 Ksenija Smoljak Kalamir verfasserin aut New Diamond-<i<α</i< Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula<-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<σ</mi<</semantics<</math<</inline-formula<-finite measures in time scale calculus. Moreover, as a special case, we obtain these inequalities for the delta and the nabla integral. By using the relation between calculus on time scales <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<T</mi<</semantics<</math<</inline-formula< and differential calculus on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<R</mi<</semantics<</math<</inline-formula<, we obtain already-known Steffensen-type inequalities. time scales diamond-α integral measure spaces Steffensen-type inequality convex function Mathematics In Axioms MDPI AG, 2012 11(2022), 7, p 323 (DE-627)718622030 (DE-600)2661511-3 20751680 nnns volume:11 year:2022 number:7, p 323 https://doi.org/10.3390/axioms11070323 kostenfrei https://doaj.org/article/0455f9e1cc9b4a3c8d5e7d8a2c673dfa kostenfrei https://www.mdpi.com/2075-1680/11/7/323 kostenfrei https://doaj.org/toc/2075-1680 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 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_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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 11 2022 7, p 323
allfieldsSound	10.3390/axioms11070323 doi (DE-627)DOAJ028499018 (DE-599)DOAJ0455f9e1cc9b4a3c8d5e7d8a2c673dfa DE-627 ger DE-627 rakwb eng QA1-939 Ksenija Smoljak Kalamir verfasserin aut New Diamond-<i<α</i< Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula<-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<σ</mi<</semantics<</math<</inline-formula<-finite measures in time scale calculus. Moreover, as a special case, we obtain these inequalities for the delta and the nabla integral. By using the relation between calculus on time scales <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<T</mi<</semantics<</math<</inline-formula< and differential calculus on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<R</mi<</semantics<</math<</inline-formula<, we obtain already-known Steffensen-type inequalities. time scales diamond-α integral measure spaces Steffensen-type inequality convex function Mathematics In Axioms MDPI AG, 2012 11(2022), 7, p 323 (DE-627)718622030 (DE-600)2661511-3 20751680 nnns volume:11 year:2022 number:7, p 323 https://doi.org/10.3390/axioms11070323 kostenfrei https://doaj.org/article/0455f9e1cc9b4a3c8d5e7d8a2c673dfa kostenfrei https://www.mdpi.com/2075-1680/11/7/323 kostenfrei https://doaj.org/toc/2075-1680 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 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_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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 11 2022 7, p 323
language	English
source	In Axioms 11(2022), 7, p 323 volume:11 year:2022 number:7, p 323
sourceStr	In Axioms 11(2022), 7, p 323 volume:11 year:2022 number:7, p 323
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	time scales diamond-α integral measure spaces Steffensen-type inequality convex function Mathematics
isfreeaccess_bool	true
container_title	Axioms
authorswithroles_txt_mv	Ksenija Smoljak Kalamir @@aut@@
publishDateDaySort_date	2022-01-01T00:00:00Z
hierarchy_top_id	718622030
id	DOAJ028499018
language_de	englisch
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callnumber-first	Q - Science
author	Ksenija Smoljak Kalamir
spellingShingle	Ksenija Smoljak Kalamir misc QA1-939 misc time scales misc diamond-α integral misc measure spaces misc Steffensen-type inequality misc convex function misc Mathematics New Diamond-<i<α</i< Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces
authorStr	Ksenija Smoljak Kalamir
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topic_title	QA1-939 New Diamond-<i<α</i< Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces time scales diamond-α integral measure spaces Steffensen-type inequality convex function
topic	misc QA1-939 misc time scales misc diamond-α integral misc measure spaces misc Steffensen-type inequality misc convex function misc Mathematics
topic_unstemmed	misc QA1-939 misc time scales misc diamond-α integral misc measure spaces misc Steffensen-type inequality misc convex function misc Mathematics
topic_browse	misc QA1-939 misc time scales misc diamond-α integral misc measure spaces misc Steffensen-type inequality misc convex function misc Mathematics
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title	New Diamond-<i<α</i< Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces
ctrlnum	(DE-627)DOAJ028499018 (DE-599)DOAJ0455f9e1cc9b4a3c8d5e7d8a2c673dfa
title_full	New Diamond-<i<α</i< Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces
author_sort	Ksenija Smoljak Kalamir
journal	Axioms
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author-letter	Ksenija Smoljak Kalamir
doi_str_mv	10.3390/axioms11070323
title_sort	new diamond-<i<α</i< steffensen-type inequalities for convex functions over general time scale measure spaces
callnumber	QA1-939
title_auth	New Diamond-<i<α</i< Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces
abstract	In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula<-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<σ</mi<</semantics<</math<</inline-formula<-finite measures in time scale calculus. Moreover, as a special case, we obtain these inequalities for the delta and the nabla integral. By using the relation between calculus on time scales <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<T</mi<</semantics<</math<</inline-formula< and differential calculus on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<R</mi<</semantics<</math<</inline-formula<, we obtain already-known Steffensen-type inequalities.
abstractGer	In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula<-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<σ</mi<</semantics<</math<</inline-formula<-finite measures in time scale calculus. Moreover, as a special case, we obtain these inequalities for the delta and the nabla integral. By using the relation between calculus on time scales <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<T</mi<</semantics<</math<</inline-formula< and differential calculus on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<R</mi<</semantics<</math<</inline-formula<, we obtain already-known Steffensen-type inequalities.
abstract_unstemmed	In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula<-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<σ</mi<</semantics<</math<</inline-formula<-finite measures in time scale calculus. Moreover, as a special case, we obtain these inequalities for the delta and the nabla integral. By using the relation between calculus on time scales <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<T</mi<</semantics<</math<</inline-formula< and differential calculus on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi mathvariant="double-struck"<R</mi<</semantics<</math<</inline-formula<, we obtain already-known Steffensen-type inequalities.
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container_issue	7, p 323
title_short	New Diamond-<i<α</i< Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces
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up_date	2024-07-03T17:54:55.063Z
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