On Family of Totally Ordered Interval Valued ConvexMappings and Applications

Inequalities have been examined from multiple viewpoints to identify novel developments and ramifications.One of the prominent strategies in the following area is the development of new unified representationsinvolving various rectified forms of convexity and fractional calculus. Numerous fundamental inequalities,like Hermite-Hadamard, Ostrowski’s, and H¨older’s types, have been assessed in recent years regarding set-valued maps based on various ordering relations. In the progressive article, we define a novel family ofconvex mappings incorporating center-radius relations and quasi-means. The effectiveness of this class isdemonstrated by the fact that by specifying various values of H and ω, we obtain various known and newclasses of I.V. convexity connecting with cr-ordering relations. Furthermore, we construct new genericversions of the Jensen’s like inequalities Hermite-Hadamard(H-H) inequality, Hermite-Hadamard-Fejer(H-H-F) inequality, and product form H-H inequality deploying the freshly proposed class of I.V. convexity andclassical R-L fractional operators. The validation of obtained results is explained with the help of graphicalillustrations and numerical examples. Also, we provide the applications to special means and informationtheory. Mathematics Subject Classification (2010): 26A33; 26A51; 26D07; 26D10; 26D15; 26D20.