An extension of Matkowski’s and Wardowski’s fixed point theorems with applications to functional equations

Fixed point theorems to generalize FR- contraction mappings with application to nonlinear matrix equations

“…Wardowski [26] generalized the Banach contraction principle by introducing the notion of F-contraction on metric spaces. The result of Wardowski was further extended and generalized by several authors (see [10], [11], [12], [17], [19], [27] and references therein) by improving the condition of F-contraction .…”

“…It asserts that every contraction mapping on a complete metric space possesses a unique …xed point. Several extensions of this principle were considered by many authors to various generalized contractions and di¤erent type of spaces (see [1], [3], [4], [5], [6], [8], [10], [12], [18], [20], [21], [26]). Wardowski [26] generalized the Banach contraction principle by introducing the notion of F-contraction on metric spaces.…”

Matkowski-Type Functional Contractions under Locally Transitive Binary Relations and Applications to Singular Fractional Differential Equations

“…Order-theoretic variants of the Matkowski fixed point theorem were studied by Agarwal et al [6] and O'Regan and Petruşel [7], which were then further enriched by Aydi et al [8] to prove certain tripled coincidence point theorems. On the other hand, Khantwal and Gairola [9] presented a fixedpoint theorem for a system of mappings on the finite product of metric spaces employing the concept of the comparison function and utilized the same to solve a system of functional equations. Very recently, Barcz [10] provided a new proof of the Matkowski fixed-point theorem using Cantor's intersection theorem instead of Picard iterations.…”