Common fixed point theorems of integral type contraction on metric spaces and its applications to system of functional equations

Abstract

In this article, using the common (CLR) property, common fixed point results for two pairs of weakly compatible mappings satisfying contractive condition of integral type on metric spaces are established. Furthermore, the existence and uniqueness of common solution for system of functional equations arising in dynamic programming are discussed as an application of a common fixed point theorem presented in this paper. MSC: 47H10; 54H25

Fixed points of weakly compatible mappings satisfying a generalized common limit range property

“…Several results are produced from the main result as special cases. These results generalize the work in [23], and many others in the available literature.…”

“…Stojakovic et al [25] generalized the concept of the Banach's FPT by the help of integral type contractions by following the work due to Nadler [22]. Sarwar et al [23] produced an FPT by the help of integral type contractions and provided some applications of their results in dynamic programing. For the applications of the FPTs in fractional differential equations, we refer the readers to [6,8,15] and some other related results can be studied in [16,19].…”

Common Fixed Point Theorem via Cyclic (α,β)–(ψ,φ)S-Contraction with Applications

“…On the other hand, the existence of unique solutions to functional equations has been examined using various fixed point results (see [25,26] and the references therein). In particular, Isik et al [19] and Latif et al [20] studied the existence of a unique bounded common solution to the following system of functional equations:…”

Common fixed point results involving contractive condition of integral type in complex valued metric spaces

“…Manro et al [18] proved common fixed point theorems satisfying integral type contractive condition using the (E.A) and (CLR) properties in complex valued metric space which generalize the noted theorem of Branciari [9]. In recent years, the theorem of Branciari [9] had also been generalized to two pairs of weakly compatible mappings, by several authors in metric spaces, which include [4,5,11,14,17,21] and some others.…”