Fixed point theorems on ordered gauge spaces with applications to nonlinear integral equations

Abstract

We establish coincidence and fixed point theorems for mappings satisfying generalized weakly contractive conditions on the setting of ordered gauge spaces. Presented theorems extend and generalize many existing studies in the literature. We apply our obtained results to the study of existence and uniqueness of solutions to some classes of nonlinear integral equations.

Common fixed points of mappings satisfying implicit contractive conditions

“…See, also [42][43][44][45], and references therein. A common fixed point result in ordered metric spaces for mappings satisfying implicit contractive conditions is given by the next theorem.…”

Tripled coincidence point results for generalized contractions in ordered generalized metric spaces

“…Very recently, inspired from the notion of weak j-contractions, a new concept of ( ψ, j)-contractions was introduced (see e.g. [3][4][5][6][7]). …”

Fixed point theorems for multivalued G-contractions in Hausdorff b-Gauge spaces

“…Frigon [14] and Chis and Precup [10] generalized the Banach contraction principle on gauge spaces. Some interesting results are also been obtained by the authors: Agarwal et al [1], Chifu and Petrusel [9], Cherichi et al [8,7], Lazara and Petrusel [18], Jleli et al [16].…”