Fisher type fixed point results in controlled metric spaces

Abstract

In the present paper, we define a rational contractive condition of Fisher type in the context of controlled metric space and obtain some generalized fixed point results in this space. These results will unify and amend many well-known results of literature. Some consequences and an example has been presented at the end to show the authenticity of the established results.

Common α-Fuzzy Fixed Point Results for F-Contractions with Applications

“…Many researchers [19][20][21]25] established several types of fixed point results by using and extending the F-contraction. In the framework of b-metric space, Cosentino et al [22] added a new condition (F 4 ) and opened a new area of research in this way:…”

Multidimensional fixed points in generalized distance spaces

“…Most of the problems of applied mathematics are reduced to finding fixed points of certain mappings. For solving various problems of integral calculus, researchers have tried to generalize contractive conditions, mappings, and metric spaces, see [6][7][8][9][10][11]17]. Clearly, G ∈ C(I).…”

Reich-Type and (α, F)-Contractions in Partially Ordered Double-Controlled Metric-Type Spaces with Applications to Non-Linear Fractional Differential Equations and Monotonic Iterative Method

“…Mlaiki et al [15] introduced the notion of controlled-type metric spaces by replacing b ≥ 1 with a controlled function β : Ξ × Ξ → [1, +∞) in the triangular inequality of b-metric space. Lateef [16] defined a Fisher-type contractive condition by using the idea of controlled metric-type spaces and obtained some generalized fixed-point results. In addition, he established some interesting examples to show the authenticity of the established results.…”