New Fixed-Point Results in Controlled Metric Type Spaces with Applications

被引:0
作者
Souayah, Nizar [1 ]
Hidri, Lotfi [2 ]
机构
[1] King Saud Univ, Community Coll Al Riyadh, Dept Nat Sci, Riyadh 11421, Saudi Arabia
[2] King Saud Univ, Coll Engn, Ind Engn Dept, Riyadh 11421, Saudi Arabia
关键词
fixed point; controlled metric space; graph theory; differential equation; MAPPINGS; CONTRACTION; PRINCIPLE; DISTANCE; THEOREMS;
D O I
10.3390/axioms14020085
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this manuscript, we present several novel results in fixed-point theory for a complete controlled metric space. The first presented result is inspired from the Caristi contraction where we explore the existence and uniqueness of fixed points under specific conditions. Furthermore, we propose a graphical form of it by endowing the considered space with a graph and develop a new fixed-point theorem, which is illustrated by two examples. Also, we establish a theorem for the alpha-admissible mapping. To demonstrate its effectiveness, the last theorem proposes an approach to solve a second-order differential equation.
引用
收藏
页数:16
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