Hermite–Hadamard Type Inequalities for Interval-Valued Preinvex Functions via Fractional Integral Operators

• DOI: 10.1007/s44196-021-00061-6
• Publication Date: 2022-01-19T18:02:55Z
• Authors: Hari Mohan Srivas...; Soubhagya Kumar S...; Pshtiwan Othman M...; Dumitru Baleanu; Bibhakar Kodamasingh
• Keywords: Interval (graph theory); Social Sciences; Convex Functions; Multi-Criteria Decision Making; Management Science and Operations Research; Operator (biology); Matrix Inequalities and Geometric Means; Mathematical analysis; Biochemistry; Gene; 01 natural sciences; Decision Sciences; Fractional Integrals; Riemann integral; FOS: Mathematics; 0101 mathematics; Fourier integral operator; Biology; Hadamard transform; Hermite polynomials; Ecology; Applied Mathematics; Fractional calculus; Pure mathematics; Operator theory; Iterative Algorithms for Nonlinear Operators and Optimization; Applied mathematics; Chemistry; Computational Theory and Mathematics; Inequality; Combinatorics; FOS: Biological sciences; Physical Sciences; Computer Science; Repressor; Hermite-Hadamard Inequalities; Transcription factor; Type (biology); Mathematics

AbstractIn this article, the notion of interval-valued preinvex functions involving the Riemann–Liouville fractional integral is described. By applying this, some new refinements of the Hermite–Hadamard inequality for the fractional integral operator are presented. Some novel special cases of the presented results are discussed as well. Also, some examples are presented to validate our results. The established outcomes of our article may open another direction for different types of integral inequalities for fractional interval-valued functions, fuzzy interval-valued functions, and their associated optimization problems.