Abstract

In this paper, we present two main results about best proximity points for multivalued mappings. First, taking into account Klim and Wardowski’s approach in fixed-point theory, we obtain a new result for multivalued mappings which includes the main theorem of Kamran [Kamranm, T. (2009). Mizoguchi–Takahashi’s type fixed point theorem. Comput. Math. Appl. 57(3):507–511]. Second, combining this approach with cyclic contraction, we give a general best proximity point result, and so we obtain many well-known fixed-point theorems such as Mizoguchi–Takahashi, Feng–Liu and Klim–Wardowski [Mizoguchi, N., Takahashi, W. (1989). Fixed point theorems for multivalued mappings on complete metric spaces. J. Math. Anal. Appl. 141(1):177–188; Feng, Y., Liu, S. (2006). Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings. J. Math. Anal. Appl. 317(1):103–112; Klim, D., Wardowski, D. (2007). Fixed point theorems for set-valued contractions in complete metric spaces. J. Math. Anal. Appl. 334(1):132–139]. Also, we support our results by providing some nontrivial, illustrative and comparative examples.

摘要

在本文中，我们提出了关于多值映射的最佳邻近点的两个主要结果。首先，考虑到 Klim 和 Wardowski 在不动点理论中的方法，我们获得了多值映射的新结果，其中包括 Kamran [Kamranm, T. (2009) 的主要定理。Mizoguchi-Takahashi 类型不动点定理。计算。数学。应用程序 57（3）：507-511]。其次，将此方法与循环收缩相结合，我们给出了一般的最佳邻近点结果，因此我们获得了许多著名的不动点定理，例如 Mizoguchi-Takahashi、Feng-Liu 和 Klim-Wardowski [Mizoguchi, N., Takahashi , W. (1989)。完全度量空间上多值映射的不动点定理。J. 数学。肛门。应用程序 141（1）：177-188；Feng, Y., Liu, S. (2006)。多值收缩映射和多值 Caristi 类型映射的不动点定理。J. 数学。肛门。应用程序 317（1）：103-112；Klim, D., Wardowski, D. (2007)。完全度量空间中集合值收缩的不动点定理。J. 数学。肛门。应用程序 334（1）：132-139]。此外，我们通过提供一些重要的、说明性的和比较的例子来支持我们的结果。