On the Existence of Coincidence and Common Fixed Point of Two Rational Type Contractions and an Application in Dynamical Programming

Abstract

In this work, we establish some coincidence point results for self-mappings satisfying rational type contractions in generalized metric spaces in the sense of Branciari [7]. Presented coincidence point theorems weak and extend numerous existing theorems in the literature besides furnishing some illustrative examples for our results. Finally, our results applies, in particular, to the study of solvability of functional equations arising in dynamic programming.

A Multidimensional Fixed‐Point Theorem and Applications to Riemann‐Liouville Fractional Differential Equations

“…For more information about coupled, tripled, and -tupled fixed points, see [9][10][11][12][13][14][15][16][17]. Now, we recall some definitions about the fractional derivative.…”

Some Results on N-Tupled Coincidence and Fixed Points of Graphs on Metric Spaces and an Application to Integral Equations

“…The theory of fixed point has become very important and useful to solve many mathematical problems in different subjects of sciences such as dynamical programming [1], optimization theory [2], signal processing [3], and iterative process [4], and other times it is used to prove the existence of solution of differential and integral equations [5,6].…”