Fixed Point Results for Almost Generalized Cyclic (ψ, φ)‐Weak Contractive Type Mappings with Applications

Abstract

We define a class of almost generalized cyclic(ψ,ϕ)-weak contractive mappings and discuss the existence and uniqueness of fixed points for such mappings. We present some examples to illustrate our results. Moreover, we state some applications of our main results in nonlinear integral equations.

On Fixed Point Theorem of C Class Functions - B Weak Cyclic Mappings

“…The fixed point theorem given in (Karapinar and Sadarangani, 2012) focused on a wider class of metric spaces. Jleli et al (2014;Karapinar et al, 2012b) generalized the results to cyclic (φ, ϕ)-weak contractions in some other metric spaces.…”

Nonlinear generalized cyclic contractions in complete G-metric spaces and applications to integral equations

“…Therefore by (III), we deduce that, for each t ∈ Using the same technique, we can show that the above inequality also holds if we take (u, v, w) ∈ A 2 × A 1 × A 1 . Consequently, by Corollary 1, f has a unique fixed point u * ∈ A 1 ∩ A 2 , that is, u * ∈ C is the unique solution to (17).…”

“…Kirk et al obtained, among others, cyclic versions of the Banach contraction principle [1], of the Boyd and Wong fixed point theorem [4] and of the Caristi fixed point theorem [5]. Following the paper [3], a number of fixed point theorems on cyclic representation of Y with respect to a self-mapping f have appeared (see, e.g., [6][7][8][9][10][11][12][13][14][15][16][17]).…”

Common Fixed Points of Generalized Cyclic Meir-Keeler-Type Contractions in Partially Ordered Metric Spaces

“…Case 1. Suppose that 2 = 2 +1 for some ∈ N in the inequality (16). Since 2 and 2 +1 are comparable in with 2 ∈ and 2 +1 ∈ , by the Remark 9, we have…”