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.
Highlights
Fixed point theory is a crucial tool in the analysis of nonlinear problems
Ciricet al. 7 proved some fixed point results in ordered metric spaces using almost generalized contractive condition, which is given in the following definition
We introduce a class of almost generalized cyclic ψ, φ -weak contractive mappings and we investigate the existence and uniqueness of fixed points for almost generalized cyclic ψ, φ -weak contractive type mappings
Summary
Banach contraction mapping principle 1 is the most known result in this direction: A self-mapping T : X → X on a complete metric space X, d has a unique fixed point if there exists k ∈ 0, 1 such that d T x, T y ≤ kd x, y for all x, y ∈ X. In this theorem, a self-mapping T is necessarily continuous. 7 proved some fixed point results in ordered metric spaces using almost generalized contractive condition, which is given in the following definition. We apply our main result to analyze the existence and uniqueness of solutions for a class of nonlinear integral equations
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