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We give a generalized version of the well-known Borsuk’s antipodal fixed point theorem for a large class of antipodally approachable condensing or compact set-valued maps defined on closed subsets of locally convex topological vector spaces. These results contain corresponding results obtained in the literature for compact set-valued maps with convex values.

In this paper, we consider a production economy with an unbounded attainable set where the consumers may have non-complete non-transitive preferences. To get the existence of an equilibrium, we provide an asymptotic property on preferences for the attainable consumptions and we use a combination of the nonlinear optimization and fixed point theorems on truncated economies together with an asymptotic argument. We show that this condition holds true if the set of attainable allocations is compact or, when the preferences are representable by utility functions, if the set of attainable individually rational utility levels is compact. This assumption generalizes the CPP condition of [N. Allouch, An equilibrium existence result with short selling, J. Math. Econom. 37 2002, 2, 81–94] and covers the example of [F. H. Page, Jr., M. H. Wooders and P. K. Monteiro, Inconsequential arbitrage, J. Math. Econom. 34 2000, 4, 439–469] when the attainable utility levels set is not compact. So we extend the previous existence results with non-compact attainable sets in two ways by adding a production sector and considering general preferences.

We are concerned with the study of a class of non-autonomous eigenvalue problems driven by two non-homogeneous differential operators with variable (p1,p2){(p_{1},p_{2})}-growth. The main result of this paper establishes the existence of a continuous spectrum consisting in an unbounded interval and the nonexistence of eigenvalues in a neighbourhood of the origin. The abstract results of this paper are described by two Rayleigh-type quotients and the proofs rely on variational arguments.

Epidemiological studies on fractures in European professional football (soccer) are in abundance. However, such data are lacking in Middle Eastern professional footballers and information on fracture treatment is scarce. The aim of this study is to describe the epidemiology of fractures across seven seasons in Qatar Stars League (QSL) footballers. A prospective study of fractures in professional male footballers over 7 consecutive seasons (2013 to 2020), involving 3255 players and 106 team' seasons. Time loss and injuries and illnesses were recorded using standardised digital tools in accordance with international consensus procedures. Fractures were recorded according to onset mechanism, location, diagnoses, treatment and return to play. A total of 108 players sustained fractures during 638,247 hours of player exposure (88.9% training and 11.1% matches), representing 2.7% of all time-loss injuries. The incidence was 0.17 fractures per 1000 h of exposure (match and training incidence of 0.9 and 0.07 fractures /1000 h, respectively), equivalent to an average of one fracture per team per season. Fractures mostly occurred in the feet (28.2%), hands (21.1%), shoulders (11.3%) and head (i.e., face) (9.9%). Mean (median) absence was 71 (47 days), with 4.6% refractures. Only 34.3% of the fractures required surgery and nearly all players (98.1%) returned to play at the professional level. Almost all professional football players with fractures return to play at the same competitive level after an average of 10 weeks of absence (mean absence was 71 ± 81 (median: 47, Inter Quartile Range [14-93]) days). One in ten continue to play with symptoms and one in twenty may refracture. Long-term effects of fractures are still unknown. [ABSTRACT FROM AUTHOR]

Chebbi, S, Chamari, K, Van Dyk, N, Gabbett, T, and Tabben, M. Hamstring injury prevention for elite soccer players: A real-world prevention program showing the effect of players' compliance on the outcome. J Strength Cond Res 36(5): 1383–1388, 2022—The aim of this study was to determine the effect of implementing the Nordic hamstring exercise (NHE) to prevent hamstring injuries in soccer. A professional team was followed by the same medical team during 5 successive seasons (2012/2013 through 2016/2017). During the first and last seasons (2012/2013 and 2016/2017), no hamstring preventive action was implemented. For the seasons 2013/2014, 2014/2015, and 2015/2016, a noncompulsory (few players refusing to participate) NHE prevention program was implemented with accurate recording of the players' training and match exposure and attendance to the prevention sessions. The first 10 weeks of the season were used to progressively increase the volume and intensity of the NHE exercises, and at the end of the season, players were split in low-, moderate-, and high-attendance groups to the prevention sessions. Overall, 35 time-loss hamstring strain injuries were accounted for. The injury incidence was 0.30 per player per season, and the injury rate was 0.95 injury/1000 hour of exposure. A nonstatistically significant higher risk of hamstring injury was observed in the control, low, and moderate attendance groups compared with the high-attendance group. The greatest risk of hamstring injury was observed in the low-attendance group (odds ratio 1.77, confidence interval 0.57–5.47, p = 0.32). Implementing a NHE prevention program has a positive effect on the injury rate in a soccer team; however, the compliance of players with such interventions may be critical for its success. [ABSTRACT FROM AUTHOR]

We extend the viscosity approximation method (VAM) to accretive operators (via their resolvents) in a uniformly convex and/or uniformly Gateaux differentiable Banach space X to find a zero of an m-accretive operator and of the sum of two m-accretive operators. In all cases, we prove the strong convergence of our VAM algorithms and the limit of the iterates is identified as the unique sunny nonexpansive retraction onto to the zero set of the operator. [ABSTRACT FROM AUTHOR]

We consider an iterative method for regularization of a variational inequality (VI) defined by a Lipschitz continuous monotone operator in the case where the set of feasible solutions is decomposed to the intersection of finitely many closed convex subsets of a Hilbert space. We prove the strong convergence of the sequence generated by our algorithm. It seems that this is the first time in the literature to handle iterative solution of ill-posed VIs in the domain decomposition case. [ABSTRACT FROM AUTHOR]

In this paper, we consider a production economy with an unbounded attainable set where the consumers may have non-complete non-transitive preferences. To get the existence of an equilibrium, we provide an asymptotic property on preferences for the attainable consumptions and we use a combination of the nonlinear optimization and fixed point theorems on truncated economies together with an asymptotic argument. We show that this condition holds true if the set of attainable allocations is compact or, when the preferences are representable by utility functions, if the set of attainable individually rational utility levels is compact. This assumption generalizes the CPP condition of [N. Allouch, An equilibrium existence result with short selling, J. Math. Econom. 37 2002, 2, 81–94] and covers the example of [F. H. Page, Jr., M. H. Wooders and P. K. Monteiro, Inconsequential arbitrage, J. Math. Econom. 34 2000, 4, 439–469] when the attainable utility levels set is not compact. So we extend the previous existence results with non-compact attainable sets in two ways by adding a production sector and considering general preferences. [ABSTRACT FROM AUTHOR]

Rockafellar's proximal point algorithm is known to be not strongly convergent in general in an infinite-dimensional Hilbert space. Effort has thus been made to modify this algorithm so that strong convergence is guaranteed. In this paper we provide a strongly convergent modification of Rockafellar's proximal point algorithm in a uniformly convex Banach space which is not necessarily smooth. [ABSTRACT FROM AUTHOR]