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2016•Journal of Mathematical InequalitiesOpen access

On φ-convex functions

M‎. ‎Eshaghi Gordji, M. Rostamian Delavar, Manuel De la Sen

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Abstract

In this paper we introduce the notion of -convex functions as generalization of convex functions. Some basic results under various conditions for the function are investigated. Moreover, we establish Jensen and Hermite-Hadamard type inequalities related to -convex functions. Also, the notions of b -convex and E -convex functions, which are generalization of -convex functions are introduced and some new results related to these new settings are obtained.

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What this paper is about

In this paper we introduce the notion of -convex functions as generalization of convex functions. Some basic results under various conditions for the function are investigated. Moreover, we establish Jensen and Hermite-Hadamard type inequalities related to -convex functions. Also, the notions of b -convex and E -convex functions, which are generalization of -convex functions are introduced and some new results related to these new settings are obtained.

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Available abstract

In this paper we introduce the notion of -convex functions as generalization of convex functions. Some basic results under various conditions for the function are investigated. Moreover, we establish Jensen and Hermite-Hadamard type inequalities related to -convex functions. Also, the notions of b -convex and E -convex functions, which are generalization of -convex functions are introduced and some new results related to these new settings are obtained.

Key concepts: Mathematics, Regular polygon, Pure mathematics, Geometry

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