Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation

The concepts of convex and non-convex functions play a key role in the study of optimization. So, with the help of these ideas, some inequalities can also be established. Moreover, the principles of convexity and symmetry are inextricably linked. In the last two years, convexity and symmetry have emerged as a new field due to considerable association. In this paper, we study a new version of interval-valued functions (I-V·Fs), known as left and right χ-pre-invex interval-valued functions (LR-χ-pre-invex I-V·Fs). For this class of non-convex I-V·Fs, we derive numerous new dynamic inequalities interval Riemann–Liouville fractional integral operators. The applications of these repercussions are taken into account in a unique way. In addition, instructive instances are provided to aid our conclusions. Meanwhile, we’ll discuss a few specific examples that may be extrapolated from our primary findings.

Multiobjective fractional programming problems and the sufficient condition involving Hb – (p, r)-η- invex function

On the basis of arcwise connected convex functions and (p, r) −η - invex functions, we established Hb –(p, r) –η- invex functions. Based on the generalized invex assumption of new functions, the solutions of a class of multiobjective fractional programming problems are studied, and the sufficient optimality condition for the feasible solutions of multiobjective fractional programming problems to be efficient solutions are established and proved.

Hermite-Hadamard type inequalities for interval-valued exponential type pre-invex functions via Riemann-Liouville fractional integrals

<abstract><p>In the present research, we develop Hermite-Hadamard type inequalities for interval-valued exponential type pre-invex functions in Riemann-Liouville interval-valued fractional operator settings. Moreover, we develop He's inequality for interval-valued exponential type pre-invex functions.</p></abstract>

Geodesic $ \mathcal{E} $-prequasi-invex function and its applications to non-linear programming problems

<p style='text-indent:20px;'>In this article, we define a new class of functions on Riemannian manifolds, called geodesic <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{E} $\end{document}</tex-math></inline-formula>-prequasi-invex functions. By a suitable example it has been shown that it is more generalized class of convex functions. Some of its characteristics are studied on a nonlinear programming problem. We also define a new class of sets, named geodesic slack invex set. Furthermore, a sufficient optimality condition is obtained for a nonlinear programming problem defined on a geodesic local <inline-formula><tex-math id="M3">\begin{document}$ \mathcal{E} $\end{document}</tex-math></inline-formula>-invex set.</p>

Multiobjective Fractional Symmetric Duality in Mathematical Programming with (C,Gf)-Invexity Assumptions

In this paper, a new class of ( C , G f ) -invex functions introduce and give nontrivial numerical examples which justify exist such type of functions. Also, we construct generalized convexity definitions (such as, ( F , G f ) -invexity, C-convex etc.). We consider Mond–Weir type fractional symmetric dual programs and derive duality results under ( C , G f ) -invexity assumptions. Our results generalize several known results in the literature.

Generalized Geodesic Convexity on Riemannian Manifolds

We introduce log-preinvex and log-invex functions on a Riemannian manifold. Some properties and relationships of these functions are discussed. A characterization for the existence of a global minimum point of a mathematical programming problem is presented. Moreover, a mean value inequality under geodesic log-preinvexity is extended to Cartan-Hadamard manifolds.