In this work, we establish the concept of a new class of non-convex functions, namely hyperbolic type preinvex functions. Secondly few algebraic properties of this class are obtained. Further Hermite-Hadamard type integral inequalities are established for this class. We also derive several new inequalities for the functions for which absolute value of first derivative, with exponent greater or equal to one is hyperbolic type preinvexity. The results are obtained by using both the Hölder's inequality and Hölder-Iscan inequality and compared at the end. Several special cases are discussed as applications of the results.
Citation: Sarah Elahi, Muhammad Aslam Noor. Integral inequalities for hyperbolic type preinvex functions[J]. AIMS Mathematics, 2021, 6(9): 10313-10326. doi: 10.3934/math.2021597
In this work, we establish the concept of a new class of non-convex functions, namely hyperbolic type preinvex functions. Secondly few algebraic properties of this class are obtained. Further Hermite-Hadamard type integral inequalities are established for this class. We also derive several new inequalities for the functions for which absolute value of first derivative, with exponent greater or equal to one is hyperbolic type preinvexity. The results are obtained by using both the Hölder's inequality and Hölder-Iscan inequality and compared at the end. Several special cases are discussed as applications of the results.
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Sarah Elahi, Muhammad Aslam Noor. Integral inequalities for hyperbolic type preinvex functions[J]. AIMS Mathematics, 2021, 6(9): 10313-10326. doi: 10.3934/math.2021597
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