标题： 具有公共极限范围性质的混合广义$(F,\varphi)$-压缩的公共不动点定理及其应用 显示英文标题

标题： Common fixed point theorems for Hybrid generalized $(F,\varphi)$-contractions under common limit range property with applications

摘要： 我们考虑了一种相对较新的涉及一对映射的广义混合F-压缩，并利用它来证明一个公共不动点定理。该定理由偶尔伴随幂等的映射对满足广义$(F,\varphi)$-压缩条件，在完备度量空间中基于公共极限范围性质得到。还证明了另一个类似的定理，涉及满足有理型Hardy-Rogers$(F,\varphi)$-压缩条件的一对混合映射。我们的结果推广和改进了现有文献中的多个结果。作为我们结果的应用，我们证明了两个关于某些由动态规划和Volterra积分包含问题产生的函数方程组解的存在性定理，并提供了一个说明性的例子。 显示英文摘要

摘要： We consider a relatively new hybrid generalized F-contraction involving a pair of mappings and utilize the same to prove a common fixed point theorem for a hybrid pair of occasionally coincidentally idempotent mappings satisfying generalized $(F,\varphi)$-contraction condition under common limit range property in complete metric spaces. A similar result involving a hybrid pair of mappings satisfying a Rational type Hardy-Rogers $(F,\varphi)$-contractive condition is also proved. Our results generalize and improve several results of the existing literature. As applications of our results, we prove two theorems for the existence of solutions of certain system of functional equations arising in dynamic programming, and Volterra integral inclusion besides providing an illustrative example.