Some Results for $(s,m)$-convex Function in the Second Sense

Abstract

Convex functions, like differentiable functions, have a important role in many fields of pure and applied mathematics. It connects concepts from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. Also, inequalities for convex function has receives special attention by many researchers because the theory of convex functions has applications in different field of science like biology, economy and optimization. In this paper, it is given some properties for an (s,m)-convex function defined on [0,d], d>0 in the first sense and the second sense with m\in (0,1). Also, some integral inequalities are examined for any non positive (s,m)-convex function in the second sense with any measure space.

Keywords

• Integral inequalities;
• Measure space.
• (s;m)-convex function

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