On geodesic strongly E-convex sets and geodesic strongly E-convex functions by Kilicman, Adem, Saleh, Wedad

“…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. …”
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Notions of generalized s-convex functions on fractal sets by Kilicman, Adem, Saleh, Wedad

“…The purpose of this article is to present some new inequalities for products of generalized convex and generalized s-convex functions on fractal sets. …”
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Underapproximating backward reachable sets by semialgebraic sets by Xue, Bai, She, Zhikun, Easwaran, Arvind

“…Given a nonlinear system, a target region of simply connected compact type and a time duration, we present a method using boundary analysis to compute an UA of the backward reachable set. The UA is represented as a semialgebraic set, formed by what we term polynomial level - set functions. …”
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On product of generalized s-convex functions and new inequalities on fractal sets by Kilicman, Adem, Saleh, Wedad

“…In this article, we give some new inequalities for product of generalized s-convex functions on the co-ordinates on fractal sets. …”
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On some inequalities for generalized s-convex functions and applications on fractal sets by Kilicman, Adem, Saleh, Wedad

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Integral inequalities for s-convexity via generalized fractional integrals on fractal sets by Almutairi, Ohud, Kilicman, Adem

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A multiperson pursuit problem on a closed convex set in Hilbert space by Leong, Wah June, Ibragimov, Gafurjan

“…A differential game of pursuit of an evader by a finite number of pursuers on a closed convex set in l 2 -space is studied. The game is described by simple differential equations and players’ controls obeyed the integral constraints. …”
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Pursuit differential game of many pursuers with integral constraints on compact convex set by Ferrara, Massimiliano, Ibragimov, Gafurjan, Alias, Idham Arif, Salimi, Mehdi

“…We are given a compact convex subset of, and the pursuers and evader move in this set. …”

Non-asymptotic bounds for modified tamed unadjusted Langevin algorithm in non-convex setting by Ng, Matthew Cheng En

“…However, theoretical guarantees in Wasserstein distances for Langevin-based algorithms have traditionally been derived assuming strong convexity of the potential $U$. In this paper, we propose a novel taming factor and derive, under a non-convex setting, non-asymptotic theoretical bounds in Wasserstein-1 and Wasserstein-2 distances between the law of our algorithm, which we name the modified Tamed Unadjusted Langevin Algorithm (mTULA), and the target distribution $\pi_\beta$. …”
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Solution of a linear pursuit-evasion differential game with closed and convex terminal set. by Ibragimov, Gafurjan I., Khakestari, Marzieh, Kuchkarov, Atamurat

“…Control functions of players are subject to integral constraints. Terminal set is a closed convex subset of The Pursuer tries to bring the state of the system to the terminal set and the Evader prevents bringing of the state to the terminal set where control resource of the Pursuer is greater than that of Evader. …”
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Some generalized Hermite-Hadamardtype integral inequalities for generalizeds-convex functions on fractal sets by Kilicman, Adem, Saleh, Wedad

“…In this article, some new integral inequalities of generalized Hermite-Hadamard type for generalized s-convex functions in the second sense on fractal sets have been established.…”
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Non-asymptotic convergence bounds for modified tamed unadjusted Langevin algorithm in non-convex setting by Neufeld, Ariel, Ng, Matthew Cheng En, Zhang, Ying

“…However, theoretical guarantees in Wasserstein distances for Langevin-based algorithms have traditionally been derived assuming strong convexity of the potential U. In this paper, we propose a novel taming factor and derive, under a setting with possibly non-convex potential U and super-linearly growing gradient of U, non-asymptotic theoretical bounds in Wasserstein-1 and Wasserstein-2 distances between the law of our algorithm, which we name the modified Tamed Unadjusted Langevin Algorithm (mTULA), and the target distribution πβ. …”
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Some local fractional inequalities involving fractal sets via generalized exponential (s,m)-convexity by Saleh, Wedad, Kılıçman, Adem

Simple motion pursuit differential game of many pursuers and one evader on convex compact set by Alias, Idham Arif, Raja Ramli, Raja Noorsuria, Ibragimov, Gafurjan, Narzullaev, Anvar

“…We study a differential game of many pursuers and single evader in nonempty closed bounded convex subset of ℝn. In this game, all players cannot leave the given set. …”
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Simple motion pursuit differential game of many pursuers and one evader on convex compact set by Raja Ramli, Raja Noorsuria

“…A pursuit differential game of m pursuers and single evader in nonempty closed bounded convex subset of Rn is studied. At this juncture, all players must not leave the given set A which is subset of Rn and control parameters of all players are subjected to geometric constraints. …”
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Pursuit-evasion game of many players with coordinate-wise integral constraints on a convex set in the plane by Ferrara, Massimiliano, Gafurjan, Ibragimov, Salimi, Mehdi

“…It is assumed that the pursuers and evader move is allowed within a non empty closed convex set in the plane. Control functions of players are subject to coordinate-wise integral constraints. …”

Pursuit differential game problem with multiple players on a closed convex set with more general integral constraints by Ahmed, Idris, Kumam, Wiyada, Ibragimov, Gafurjan, Rilwan, Jewaidu

“…In this paper, we study a pursuit differential game with many but finite number of pursuers and evaders on a closed convex subset K of Rn. Players’ motion obey ordinary differential equations and confined within the set K throughout the game. …”

Expected size of random Tukey layers and convex layers by Guo, Zhengyang, Li, Yi, Pei, Shaoyu

“…We study the Tukey layers and convex layers of a planar point set, which consists of n points independently and uniformly sampled from a convex polygon with k vertices. …”
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Fractional differential calculus on riemannian manifolds and convexity problems by Wedad Saleh, Al-Lehabi

“…In addition, a new class of generalizeds-convex functions in both senses on real linear fractal sets is defined. …”
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Robust interactive image segmentation using convex active contours by Nguyen, Thi Nhat Anh, Cai, Jianfei, Zhang, Juyong, Zheng, Jianmin

“…Experimental results on a benchmark data set show that the proposed tool is highly effective and outperforms the state-of-the-art interactive image segmentation algorithms.…”
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