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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

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Generalized geometrically convex functions and inequalities.

Muhammad Aslam Noor^1,2, Khalida Inayat Noor², Farhat Safdar²

¹Department of Mathematics, King Saud University, Riyadh, Saudi Arabia.

Journal of Inequalities and Applications

|September 22, 2017

Summary

This study introduces generalized geometrically convex functions and establishes fundamental inequalities. New Hermite-Hadamard type inequalities are derived for these functions, expanding mathematical understanding.

Keywords:

Hermite-Hadamard’s type inequalities Hölder’s inequality generalized convex functions generalized geometrically convex functions

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Area of Science:

Mathematical Analysis
Convexity Theory

Background:

Convex functions are fundamental in optimization and analysis.
Generalizations of convexity extend applicability to broader function classes.

Purpose of the Study:

Introduce a novel class: generalized geometrically convex functions.
Establish foundational inequalities for this new class.
Derive new Hermite-Hadamard type inequalities.

Main Methods:

Definition and exploration of generalized geometric convexity.
Development of basic inequality proofs.
Application of established inequality frameworks to the new function class.

Main Results:

Introduction of the class of generalized geometrically convex functions.
Establishment of several basic inequalities.
Derivation of novel Hermite-Hadamard type inequalities.

Conclusions:

The study successfully defines and analyzes generalized geometrically convex functions.
New inequalities provide valuable tools for mathematical analysis.
Special cases offer further insights and potential applications.