Browsing by Author "Khan, Muhammad Bilal"

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Citation Count: Khan, Muhammad Bilal...et al. (2022). "Fuzzy-interval inequalities for generalized convex fuzzy-interval-valued functions via fuzzy Riemann integrals", AIMS Mathematics, Vol. 7, No. 1, pp. 1507-1535.
Fuzzy-interval inequalities for generalized convex fuzzy-interval-valued functions via fuzzy Riemann integrals
(2022) Khan, Muhammad Bilal; Srivastava, Hari Mohan; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Jawa, Taghreed M.; 56389
The objective of the authors is to introduce the new class of convex fuzzy-interval-valued functions (convex-FIVFs), which is known as p-convex fuzzy-interval-valued functions(p-convex-FIVFs). Some of the basic properties of the proposed fuzzy-interval-valued functions are also studied. With the help of p-convex FIVFs, we have presented some Hermite-Hadamard type inequalities (H-H type inequalities), where the integrands are FIVFs. Moreover, we have also proved the Hermite-Hadamard-Fejér type inequality (H-H Fejér type inequality) for p-convex-FIVFs. To prove the validity of main results, we have provided some useful examples. We have also established some discrete form of Jense’s type inequality and Schur’s type inequality for p-convex-FIVFs. The outcomes of this paper are generalizations and refinements of different results which are proved in literature. These results and different approaches may open new direction for fuzzy optimization problems, modeling, and interval-valued functions.©2022 the Author(s), licensee AIMS Press. © 2022, American Institute of Mathematical Sciences. All rights reserved.
Citation Count: Khan, Muhammad Bilal...et al. (2021). "Some New Fractional Estimates of Inequalities for LR-p-Convex Interval-Valued Functions by Means of Pseudo Order Relation", Axioms, Vol. 10, No. 3.
Some New Fractional Estimates of Inequalities for LR-p-Convex Interval-Valued Functions by Means of Pseudo Order Relation
(2021) Khan, Muhammad Bilal; Mohammed, Pshtiwan Othman; Noor, Muhammad Aslam; Baleanu, Dumitru; Garcia Guirao, Juan Luis; 56389
It is a familiar fact that interval analysis provides tools to deal with data uncertainty. In general, interval analysis is typically used to deal with the models whose data are composed of inaccuracies that may occur from certain kinds of measurements. In interval analysis, both the inclusion relation (subset of) and pseudo order relation (<= p) are two different concepts. In this article, by using pseudo order relation, we introduce the new class of nonconvex functions known as LR-p-convex interval-valued functions (LR-p-convex-IVFs). With the help of this relation, we establish a strong relationship between LR-p-convex-IVFs and Hermite-Hadamard type inequalities (HH-type inequalities) via Katugampola fractional integral operator. Moreover, we have shown that our results include a wide class of new and known inequalities for LR-p-convex-IVFs and their variant forms as special cases. Useful examples that demonstrate the applicability of the theory proposed in this study are given. The concepts and techniques of this paper may be a starting point for further research in this area.