We study the notions of strongly convex function as well as -strongly convex function. We present here some new integral inequalities of Jensen's type for these classes of functions. A refinement of companion inequality to Jensen's inequality established by Matić and Pečarić is shown to be recaptured as a particular instance. Counterpart of the integral Jensen inequality for strongly convex functions is also presented. Furthermore, we present integral Jensen-Steffensen and Slater's inequality for strongly convex functions.
In the article, we present several majorization theorems for strongly convex functions and give their applications in inequality theory. The given results are the improvement and generalization of the earlier results.
MSC: 26D15; 26A51; 39B62
In this article, we establish several integral majorization type and generalized Favard’s inequalities for the class of strongly convex functions. Our results generalize and improve the previous known results.
In the article, we provide an example for a η-convex function defined on rectangle is not convex, prove that every η-convex function defined on rectangle is coordinate η-convex and its converse is not true in general, define the coordinate $(\eta _{1}, \eta _{2})$(η1,η2)-convex function and establish its Hermite–Hadamard type inequality.
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