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| New Fixed Point Results over Orthogonal $\mathcal{F}$-Metric Spaces and Application in Second-Order Differential Equations |
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| KeyWord:Fixed point, orthogonal $(\alpha\theta-\beta F)$-rational contraction, cyclic $\alpha$-admissible mapping with respect to $\theta$, orthogonal $\mathcal{F}$-metric space, second-order differential equation |
| Author Name | Affiliation | | Mohammed M.A. Taleb | Department of Mathematics, Science College, Swami Ramanand Teerth Marathwada University, Nanded-431606, India
Department of Mathematics, Hodeidah University, P.O. Box 3114, Al-Hodeidah, Yemen | | Saeed A.A. Al-Salehi | Department of Mathematics, Science College, Swami Ramanand Teerth Marathwada University, Nanded-431606, India
Department of Mathematics, Aden University, P.O. Box 124, Aden, Yemen | | V.C. Borkar | Department of Mathematics, Yeshwant Mahavidyalaya, Swami Ramanand Teerth Marathwada University, Nanded-431606, India |
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| Abstract: |
| In this article, we introduce the notion of cyclic $\alpha$-admissible mapping with respect to $\theta$ with its special cases, which are cyclic $\alpha$-admissible mapping with respect to $\theta^*$ and cyclic $\alpha^*$-admissible mapping with respect to $\theta$. We present the notion of orthogonal $(\alpha\theta-\beta F)$-rational contraction and establish new fixed point results over orthogonal $\mathcal{F}$-metric space. The study includes illustrative examples to support our results. We apply our results to prove the existence and uniqueness of solutions for second-order differential equations. |
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