Browsing by Author "Korkmaz, E."

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Boundedness and Square Integrability of Solutions of Nonlinear Fourth-Order Differential Equations With Bounded Delay
(Texas State University - San Marcos, 2017) Korkmaz, E.; Tunç, C.
In this article, we give sufficient conditions for the boundedness, uniformly asymptotic stability and square integrability of the solutions to a fourth-order non-autonomous differential equation with bounded delay by using Lyapunov’s second method. © 2017 Texas State University.
The Effect of Core Training Practices on Some Strength, Lower Limb Functions and Balance Performance in Judo Athletes
(Nevzat Demirci, 2023) Yasul, Y.; Akdemır, E.; Öner, S.; Anil, B.; Korkmaz, E.; Pekesen Kurtca, M.; Yilmaz, A.K.
This study investigates the effects of core training on some strength, lower extremity functions, and balance performances in judoka. The study was based on a two-group pretest-posttest experimental design with repeated measures. The study included 12 female (F) judo athletes aged 12-18 years and 10 male (M) judo athletes aged 12-17 years. Three measurements for core strength (push-ups, planks, sit-ups), six different single leg hop tests (SLHT) for lower extremity muscle strength and YBT for balance were performed before and after 6-week core training. Shapiro-Wilk, Levene, and Paired sample t-tests were used in statistical analyses. The increases in limb symmetry index (LSI) scores were remarkable. When the push-up and plank times and sit-up scores of F and M participants were compared with the pre-test, a significant increase was observed in favor of the post-test. When we examined the dominant (D) leg hop for distance, we found that M and F judoka's SLD, THD, MSTHD, MRHD, and CHD post-test scores all increased (except F; CHD) and also M and F showed better performance in SL6MD. Similar performance outputs were seen in the non-dominant (ND) leg hop for distance measurements (only not changed F; THND). Finally, it was valuable to note that both right and left leg YBT scores showed a considerable rise in the post-test assessments. As a result, core exercise practices may improve the sit-up score by improving the time in push-ups and planks in judoka. In addition, it may improve balance performance by affecting lower extremity functions. © The Author(s) 2023.
New Results on the Qualitative Analysis of Solutions of Vides by the Lyapunov-Razumikhin Technique
(Springer, 2023) Tunc, O.; Korkmaz, E.
A new mathematical model described by a Volterra integrodifferential equation (VIDE) with constant delay is examined. New agreeable conditions on the uniformly asymptotic stability, boundedness, and square integrability of solutions of the VIDE are obtained by using the Lyapunov-Razumikhin technique. The established conditions improve some former results. They can be also regarded as nonlinear generalizations of these results. Moreover, they are weaker than some available results cited in the bibliography. Two examples are presented to demonstrate possible applications of these results and the introduced concepts. The application of the Lyapunov-Razumikhin technique leads to a significant difference and gives certain advantages over the related methods used in the books and papers cited in the bibliography.
On the Convergence of Solutions of Some Nonlinear Differential Equations of Fourth Order
(InforMath Publishing Group, 2014) Korkmaz, E.; Tunc, C.
In this paper, we consider a nonlinear differential equation of fourth order. By the Lyapunov function approach, we discuss the convergence of the solutions of the equation considered. Our findings generalize some well known results in the literature. © 2014 InforMath Publishing Group.