论文标题
在Banach空间中的一些丰富收缩
On some enriched contractions in Banach spaces
论文作者
论文摘要
在本文中，我们介绍了两种新型的丰富收缩类型，即丰富$ \ Mathcal {a} $ - 收缩和丰富$ \ Mathcal {a}'$ - 收缩。然后，我们使用映射的平均操作员的固定点属性获得了满足此类收缩的固定点。此外，我们研究了涉及收缩的固定点问题的良好性和限制的阴影特性，并给出一些示例以验证结果证明。我们构成了一个与此类收缩的固定点有关的开放问题。我们还表明，Berinde和Păcurar在各种富含收缩的情况下的最新结果以及一些众所周知的经典固定点结果是我们结果的特殊情况。
In this paper, we introduce two new types of enriched contractions, viz., enriched $\mathcal{A}$-contraction and enriched $\mathcal{A}'$-contraction. Then we obtain fixed points of mappings satisfying such contractions using the fixed point property of the average operator of the mappings. Further, we study the well-posedness and limit shadowing property of the fixed point problem involving the contractions, and give some examples to validate the results proved. We frame an open question related to the existence of a fixed point of such contractions. We also show that Berinde and Păcurar's recent results on different kinds enriched contractions and some well known classical fixed point results are particular cases of our results.
