Abstract
We establish some coincidence point results for self-mappings satisfying rational type contractions in a generalized metric space. Presented coincidence point theorems weaken and extend numerous existing theorems in the literature besides furnishing some illustrative examples for our results. Finally, our results apply, in particular, to the study of solvability of functional equations arising in dynamic programming.
Highlights
Banach contraction principle is one of the most important aspects of fixed point theory as a source of the existence and uniqueness of solutions of many problems in various branches inside and outside mathematics
In 1975, Dass and Gupta [4] defined the following rational type contraction which is more general than the contraction condition: d (Ax, Ay) ≤ ad (x, y) + bd (y, Ay) (d (x, Ax) + 1)
∀x, y ∈ X, a, b ≥ 0, a + b < 1, where A : X → X is a mapping from a metric space X into itself
Summary
Banach contraction principle is one of the most important aspects of fixed point theory as a source of the existence and uniqueness of solutions of many problems in various branches inside and outside mathematics (see, [1,2,3]). Some generalizations of this theorem replace the contraction condition by a weaker. We introduce coincidence point theorems for two contraction self-mappings of rational type in generalized metric spaces. These theoretical theorems are applied to the study of the existence solutions to a system of functional equations in dynamic programming
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