Generalization of Khan fixed point theorem

Abstract

In this paper, we study some results of existence and uniqueness of fixed points for a class of mappings satisfying an inequality of rational expressions. Our main result extends and unifies the well-known results of Khan [M. S. Khan, Rend. Inst. Math. Univ. Trieste, 8 (1976), 69-72].

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

“…Recently, Piri et al, [8] extended the results of Khan [6] and Fisher [4] by introducing a new general contractive condition with rational expressions as follows:…”

“…The Banach contraction principle provides a constructive method of finding a unique solution for models involving various types of differential and integral equations. This principle is generalized by several authors in various directions (see [1,[6][7][8] and references therein).…”

Ekeland’s Variational Principle and Minimization Takahashi’s Theorem in Generalized Metric Spaces

“…On the other hand, by using semicontinuous h(·, u) and Equation (19), we find thatū is a solution of EP.…”

“…Then, there exists y ∈ Z such that f (y) ≤ f (x); d(x, y) ≤ 1 and f (z) > f (y) − d(y, z) for all y = z. Now, we study generalized metric spaces and their properties, for more details and application, we refer to [7,[14][15][16][17][18][19][20][21][22][23].…”

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.…”