On Weighted Means and MN-convex functions
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TL;DR
This paper introduces generalized definitions of weighted means and MN-convex functions, providing broader results that encompass various convexity classes through special cases.
Contribution
It offers new, more general definitions of weighted means and MN-convex functions, extending existing convexity theories.
Findings
Generalized properties of MN-convex functions
Results applicable to various convexity classes
Unified framework for convexity analysis
Abstract
In this paper, we give more general definitions of weighted means and MN-convex functions. Using these definitions, we also obtain some generalized results related to properties of MN-convex functions. The importance of this study is that the results of this paper can be reduced to different convexity classes by considering the special cases of M and N.
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Taxonomy
TopicsMathematical Inequalities and Applications · Functional Equations Stability Results · Optimization and Variational Analysis