On geodesic strongly E-convex sets and geodesic strongly E-convex functions

Abstract

In this article, geodesic E-convex sets and geodesic E-convex functions on a Riemannian manifold are extended to the so-called geodesic strongly E-convex sets and geodesic strongly E-convex functions. Some properties of geodesic strongly E-convex sets are also discussed. The results obtained in this article may inspire future research in convex analysis and related optimization fields.MSC: 52A20; 52A41; 53C20; 53C22

Generalized Geodesic Convexity on Riemannian Manifolds

“…The geodesic geodesic E-convexity was proposed on a Riemannian manifold in [20]. These results were further generalized in [21][22][23]. Recently, Ahmad et al [24] have discussed the geodesic sub-b-s convex functions and studied characterizations of these functions.…”

On properties of geodesic semilocal E-preinvex functions

“…Moreover, geodesic semi E-convex (GsEC) functions were introduced [21]. Recently, geodesic strongly E-convex (GSEC) functions were introduced and some of their properties were discussed [22].…”

Non-differentiable Solutions for Local Fractional Nonlinear Riccati Differential Equations

“…Ordinary differential equations (ODE) via local fractional derivatives [1] have played an important role in applied science, such as in fractal damped vibrations [2], growth of populations [3], and fractal heat transfers [4]. The local fractional calculus is useful to describe diffusion [5][6][7][8], heat conduction [9], waves [10][11][12], and other phenomena [13]. In [14] the nonlinear Riccati differential equation (NRDE) is written in the form dΛ (µ)…”

“…where ζ is the fractal dimension of the local fractional operator [1][2][3][4][5][6][7][8][9][10][11][12][13], ̟ 0 (µ) = 0 and ̟ 2 (µ) = 0. Our main aim is to study non-differentiable solutions of LFNRDE.…”