Rasham Tahair, Panda Sumati Kumari, Basendwah Ghada Ali, Hussain Aftab
Department of Mathematics, University of Poonch Rawalakot, Azad Kashmir, Pakistan.
Department of Mathematics, GMR Institute of Technology, Rajam, 532127, Andhra Pradesh, India.
Heliyon. 2024 Jul 4;10(14):e34078. doi: 10.1016/j.heliyon.2024.e34078. eCollection 2024 Jul 30.
In the context of complete strong -metric-like spaces, we prove new multi-fixed point solutions for the pair of multivalued, dominated operators that fulfill the generalized nonlinear contractions on a closed ball. We employ a mix of two different types of mappings in our approach: one is a class of multi-dominated mappings, while the other is a weaker class of strictly increasing mappings. Additionally, some new fixed-point results concerning the multi-graph-dominated structure in graph contraction are presented. To validate the hypothesis of acquired results, a few sample cases are presented. A numerical experiment has been carried out to approximate the fixed point. In addition, to demonstrate the originality of our findings, we proposed simple and efficient solutions to the system of fractional differential equations and nonlinear Volterra-type integral equations.
在完备的强类度量空间的背景下，我们证明了一对多值、占优算子在闭球上满足广义非线性收缩的新的多不动点解。我们在方法中采用了两种不同类型映射的混合：一种是一类多占优映射，而另一种是较弱的严格递增映射类。此外，还给出了一些关于图收缩中多图占优结构的新的不动点结果。为了验证所得结果的假设，给出了一些示例情况。进行了数值实验以逼近不动点。此外，为了证明我们发现的原创性，我们提出了分数阶微分方程和非线性Volterra型积分方程组的简单有效解。
