Common fixed point theorems for rational F R $F_{\mathcal{R}}$ -contractive pairs of mappings with applications

Abstract

In this paper, we study the existence of solution for the following non-linear matrix equations:

On (Λ,Υ,ℜ)-Contractions and Applications to Nonlinear Matrix Equations

“…Next corollaries (Corollary 5 and Corollary 6) generalize fixed point theorems given by Wardowski [22] (Theorem 1) and Zada and Sarwar [33].…”

“…Recently, Al-Sulami et al [34] investigated fixed points of Θ-contractions under the effect of binary relation in complete metric spaces. Similarly, Zada and Sarwar [33] considered F-contractions under an arbitrary binary relation and proved some related fixed point results.…”

“…Definition 7. [33] Let φ, ψ : → be two self-mappings on a non-empty set. Then a binary relation on is said (φ, ψ)-closed if for any σ, ς ∈ , we have…”

Analytical Solution for Differential and Nonlinear Integral Equations via F ϖ

“…There are developments to translate fixed point theorems into nonlinear integral equations and differential equations (for related works and developments, see [7][8][9][10][11][12][13][14][15][16][17][18][19][20]).…”

Positive coincidence points for a class of nonlinear operators and their applications to matrix equations

“…The coincidence point theory is a powerful tool in nonlinear analysis for solving a wide range of nonlinear equations arising from various applications in engineering, economics and mechanics, see for instance [1][2][3][4][5][6][7][8]. In particular, nonlinear equations in Banach spaces involving α-concave and α (− )-convex operators are considered in [9][10][11][12][13][14][15] and some references therein.…”