发表机构
Kent State University; Tarleton State University（肯特州立大学; 塔克伦州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在完备b-度量空间中，通过引入距离依赖控制函数与p阶迭代，改进推广了Chaib等人的Hardy-Rogers型不动点定理，给出p-Hardy-Rogers型多值映射的存在唯一性结论并附实例验证。
AI 中文摘要
本文在完备b-度量空间中建立了p-Hardy-Rogers型多值映射新的存在性与唯一性定理。我们的方法将压缩条件中的传统常系数替换为依赖距离的控制函数，并引入p阶迭代格式，从而提供了更通用灵活的结构，涵盖了更广泛的多值算子类。我们的研究成果通过放宽所需假设、将h-上半连续性纳入假设并考虑映射的p次迭代，显著改进并推广了Chaib等人（2026）得到的Hardy-Rogers型不动点定理。文中提供了若干实例以说明我们结果的适用性。
英文摘要
In this paper, we establish new fixed point theorems for multivalued mappings satisfying Hardy-Rogers type contractive conditions in complete $b$-metric spaces. Motivated by the constant-coefficient framework of Chaib et al. (Fixed Point Theory 27 (2026), 209-228), we develop a distance-dependent formulation in which the contractive coefficients are nonnegative functions of the interpoint distance. We introduce a piecewise contraction factor corresponding to the two cases determined by the relative sizes of the cross terms in the Hardy-Rogers inequality, thereby providing a formulation adapted to the structure of the contractive condition. Under appropriate assumptions on the coefficient functions, we establish fixed point existence through either $h$-upper semicontinuity or asymptotic limsup conditions. The resulting framework yields corresponding fixed point theorems for multivalued Reich, Kannan, and Chatterjea-type contractions. We further investigate strict fixed points and obtain conditions under which the fixed point and strict fixed point sets coincide and consist of a unique point. In addition, we establish a fixed point transfer result for suitable finite iterates, showing that the contractive condition may be imposed on $T^p$ rather than on the original mapping, provided that the latter has a strict fixed point. Corresponding single-valued consequences are also derived. Several examples illustrate the applicability of the results and demonstrate situations in which the proposed conditions apply beyond the corresponding existing formulations.
Comments24
