A fixed point theorem for F-Khan-contractions on complete metric spaces and application to integral equations

Abstract

In this article, we introduce a new concept of contraction called F-Khan-contractions and prove a fixed point theorem concerning this contraction which generalizes the results announced by Khan [M. S. Khan, Rend.

Generalized multivalued Khan-type ( ψ , ϕ ) $(\psi ,\phi )$ -contractions in complete metric spaces

“…We define and examine some new generalized multivalued Khan-type contraction which extends all of F-contraction and θ -contraction studied previously. The results presented in this paper improve and extend the corresponding results in Piri et al [19], Jleli et al [18] and Altun et al [4].…”

“…Combined with the ideas from the F-contraction and the Khan-type contraction, in 2017, Piri, Rahrovi, Marasi and Kumam [19] investigated and developed the so-called F-Khan-contraction and proved the desired fixed point theorem. The results of Piri et al extended and improved Wardowski's work in [16].…”

New Types of F-Contraction for Multivalued Mappings and Related Fixed Point Results in Abstract Spaces

“…Piri et al [42] extended the results of Khan [43] and Fisher [44] by introducing a new general contractive condition with rational expressions. Recently, Piri et al [30] improved some fixed point results of -Khan type self-mapping on complete metric spaces. In this section, we introduce a new type of contraction satisfying an inequality of rational expressions and prove a new fixed point theorem concerning this type of contraction.…”

“…Wardowski [21] generalized many fixed point results in a beautiful way by introducing −contraction (see also [6,[22][23][24][25][26][27][28][29][30]). Nadler [31] extended Banach's contraction mapping principle to a fundamental fixed point theorem for multivalued mappings.…”

Fixed Point Theorems for Generalized Ψ-φ-Khan-contractions in b-rectangular Metric Spaces

“…In [10], they also studied some results of existence and uniqueness of fixed points for a class of mappings satisfying an inequality of rational expressions. Hossein Piri et al [11] introduced the concept of F-Khan-contractions and proved a fixed point theorem in complete metric spaces. Moreover, Ansari et al [12] proved C-class function on Khan type common fixed point theorems in generalized metric space.…”