Abstract
In this paper, we use ω -distance to prove the existence, uniqueness, and iterative approximations of fixed points for a few contractive mappings of integral type in complete metric spaces. The proved results are used to investigate the solvability of certain nonlinear integral equations. Four examples are given.
Highlights
The researchers [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] attained various generalizations of the well-known Banach contraction principle
Liu et al [14] obtained several fixed point theorems for contractive mappings of integral type in complete metric spaces
Kada et al [8] introduced the concept of ω-distance in metric spaces and proved a few fixed point theorems for some contractive mappings by using ω-distance
Summary
The researchers [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] attained various generalizations of the well-known Banach contraction principle. Liu et al [14] obtained several fixed point theorems for contractive mappings of integral type in complete metric spaces. Kada et al [8] introduced the concept of ω-distance in metric spaces and proved a few fixed point theorems for some contractive mappings by using ω-distance. The researchers in [3, 5,6,7, 9, 10, 17] got several fixed point results for certain contractive mappings with respect to ω-distance. We prove the existence, uniqueness, and iterative approximations of fixed points for several kinds of mappings, which satisfy some contractive conditions of integral type with respect to ω-distance in complete metric spaces. Our results generalize or differ from the corresponding fixed point theorems in [1, 14, 15]
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