Some Properties of Generalized Strongly Harmonic Convex Functions

Some Properties of Generalized Strongly Harmonic Convex Functions

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In this paper, we introduce a new class of harmonic convex functions with respect to an arbitrary trifunction F(·,·,·): K×K×[0,1]→R, which is called generalized strongly harmonic convex functions. We study some basic properties of strongly harmonic convex functions. We also discuss the sufficient co...

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Main Authors: Muhammad Aslam Noor, Khalida Inayat Noor, Sabah Iftikhar, Farhat Safdar
Format: Article
Language:English
Published: Etamaths Publishing 2018-05-01
Series:International Journal of Analysis and Applications
Online Access:http://www.etamaths.com/index.php/ijaa/article/view/1685
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spelling doaj-c665f32ab2344e948a3d2c34367586312020-11-25T00:44:41ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392018-05-01163427436313Some Properties of Generalized Strongly Harmonic Convex FunctionsMuhammad Aslam Noor0Khalida Inayat Noor1Sabah Iftikhar2Farhat SafdarCOMSATS Institute of Information Technology, IslamabadCOMSATS Institute of Information technologyCOMSATS Institute of Information TechnologyIn this paper, we introduce a new class of harmonic convex functions with respect to an arbitrary trifunction F(·,·,·): K×K×[0,1]→R, which is called generalized strongly harmonic convex functions. We study some basic properties of strongly harmonic convex functions. We also discuss the sufficient conditions of optimality for unconstrained and inequality constrained programming under the generalized harmonic convexity. Several special cases are discussed as applications of our results. Ideas and techniques of this paper may motivate further research in different fields.http://www.etamaths.com/index.php/ijaa/article/view/1685
collection DOAJ
language English
format Article
sources DOAJ
author Muhammad Aslam Noor
Khalida Inayat Noor
Sabah Iftikhar
Farhat Safdar
spellingShingle Muhammad Aslam Noor
Khalida Inayat Noor
Sabah Iftikhar
Farhat Safdar
Some Properties of Generalized Strongly Harmonic Convex Functions
International Journal of Analysis and Applications
author_facet Muhammad Aslam Noor
Khalida Inayat Noor
Sabah Iftikhar
Farhat Safdar
author_sort Muhammad Aslam Noor
title Some Properties of Generalized Strongly Harmonic Convex Functions
title_short Some Properties of Generalized Strongly Harmonic Convex Functions
title_full Some Properties of Generalized Strongly Harmonic Convex Functions
title_fullStr Some Properties of Generalized Strongly Harmonic Convex Functions
title_full_unstemmed Some Properties of Generalized Strongly Harmonic Convex Functions
title_sort some properties of generalized strongly harmonic convex functions
publisher Etamaths Publishing
series International Journal of Analysis and Applications
issn 2291-8639
publishDate 2018-05-01
description In this paper, we introduce a new class of harmonic convex functions with respect to an arbitrary trifunction F(·,·,·): K×K×[0,1]→R, which is called generalized strongly harmonic convex functions. We study some basic properties of strongly harmonic convex functions. We also discuss the sufficient conditions of optimality for unconstrained and inequality constrained programming under the generalized harmonic convexity. Several special cases are discussed as applications of our results. Ideas and techniques of this paper may motivate further research in different fields.
url http://www.etamaths.com/index.php/ijaa/article/view/1685
work_keys_str_mv AT muhammadaslamnoor somepropertiesofgeneralizedstronglyharmonicconvexfunctions
AT khalidainayatnoor somepropertiesofgeneralizedstronglyharmonicconvexfunctions
AT sabahiftikhar somepropertiesofgeneralizedstronglyharmonicconvexfunctions
AT farhatsafdar somepropertiesofgeneralizedstronglyharmonicconvexfunctions
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