Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function

In the paper, the authors present some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function via some classical inequalities such as Chebychev’s inequality for synchronous (or asynchronous, respectively) mappings, give a new proof of the log-convexity...

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Autores principales: Nisar, Kottakkaran Sooppy, Qi, Feng, Rahman, Gauhar, Mubeen, Shahid, Arshad, Muhammad
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6006262/
https://www.ncbi.nlm.nih.gov/pubmed/30137732
http://dx.doi.org/10.1186/s13660-018-1717-8
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author Nisar, Kottakkaran Sooppy
Qi, Feng
Rahman, Gauhar
Mubeen, Shahid
Arshad, Muhammad
author_facet Nisar, Kottakkaran Sooppy
Qi, Feng
Rahman, Gauhar
Mubeen, Shahid
Arshad, Muhammad
author_sort Nisar, Kottakkaran Sooppy
collection PubMed
description In the paper, the authors present some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function via some classical inequalities such as Chebychev’s inequality for synchronous (or asynchronous, respectively) mappings, give a new proof of the log-convexity of the extended gamma function by using the Hölder inequality, and introduce a Turán type mean inequality for the Kummer confluent k-hypergeometric function.
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spelling pubmed-60062622018-07-04 Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function Nisar, Kottakkaran Sooppy Qi, Feng Rahman, Gauhar Mubeen, Shahid Arshad, Muhammad J Inequal Appl Research In the paper, the authors present some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function via some classical inequalities such as Chebychev’s inequality for synchronous (or asynchronous, respectively) mappings, give a new proof of the log-convexity of the extended gamma function by using the Hölder inequality, and introduce a Turán type mean inequality for the Kummer confluent k-hypergeometric function. Springer International Publishing 2018-06-19 2018 /pmc/articles/PMC6006262/ /pubmed/30137732 http://dx.doi.org/10.1186/s13660-018-1717-8 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Nisar, Kottakkaran Sooppy
Qi, Feng
Rahman, Gauhar
Mubeen, Shahid
Arshad, Muhammad
Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function
title Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function
title_full Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function
title_fullStr Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function
title_full_unstemmed Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function
title_short Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function
title_sort some inequalities involving the extended gamma function and the kummer confluent hypergeometric k-function
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6006262/
https://www.ncbi.nlm.nih.gov/pubmed/30137732
http://dx.doi.org/10.1186/s13660-018-1717-8
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