Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 2 1 2021 02 01 On the reversible geodesics of a Finsler space endowed with a special deformed $(\alpha, \beta)$-metric 73 80 4270 10.22060/ajmc.2021.19522.1048 EN Laurian-Ioan Pişcoran Technical University of Cluj Napoca, North University Center of Baia Mare, Department of Mathematics and Computer Science, Victoriei 76, 430122 Baia Mare, Romania 0000-0003-2269-718X Cătălin Barbu &quot;Vasile Alecsandri&quot; National College, str. Vasile Alecsandri nr. 37, Bacau, Romania 0000-0002-2094-1938 Ali Akram Departamento de Matematica-ICE, Universidade Federal de Amazonas-UFAM, 69080-900 Manaus-AM, Brazil Department of Mathematics, King Khalid University, 9004 Abha, Saudi Arabia 0000-0002-6053-3031 Journal Article 2021 01 18 The scope of this paper is twofold. On the one hand, we will investigate the reversible geodesics of a Finsler space endowed with the deformed newly introduced $(\alpha, \beta)$-metric<br />\begin{equation}<br />F_{\epsilon}(\alpha,\beta)=\frac{\beta^{2}+\alpha^{2}(a+1)}{\alpha}+\epsilon\beta<br />\end{equation}<br />where $\epsilon$ is a real parameter with $|\epsilon|<2\sqrt{a+1}$ and $a\in \left(\frac{1}{4},+\infty\right)$; and on the other hand, we will investigate the T-tensor for this metric. Finsler $(\alpha,\beta)$-metric Deformation of an $(\alpha,\beta)$-metric $T$-Tensor https://ajmc.aut.ac.ir/article_4270_39b8f721582654655a6999aabe905204.pdf