Abstract
The aim of this paper is to establish the existence of some common fixed point results for generalized Geraghty ( α , ψ , ϕ ) -quasi contraction self-mapping in partially ordered metric-like spaces. We display an example and an application to show the superiority of our results. The obtained results progress some well-known fixed (common fixed) point results in the literature. Our main results cannot be specifically attained from the corresponding metric space versions. This paper is scientifically novel because we take Geraghty contraction self-mapping in partially ordered metric-like spaces via α − admissible mapping. This opens the door to other possible fixed (common fixed) point results for non-self-mapping and in other generalizing metric spaces.
Highlights
Fixed point theory occupies a central role in the study of solving nonlinear equations of kindsSx = x, where the function S is characterized on abstract space X
We show the generalized Geraghty (α, ψ, φ)-quasi contraction type mapping in partially ordered metric like space, we present some fixed and common fixed point theorems for such mappings in an ordered complete metric-like space
We present the notation of generalized Geraghty (α, ψ, φ)-quasi contraction self-mappings in partially ordered metric-like space
Summary
Fixed point theory occupies a central role in the study of solving nonlinear equations of kinds. Metric like spaces were revealed by Amini-Harandi [5] who proved the existence of fixed point results This interesting subject has been mediated by certain authors, for example, see References [6,7,8]. We show the generalized Geraghty (α, ψ, φ)-quasi contraction type mapping in partially ordered metric like space, we present some fixed and common fixed point theorems for such mappings in an ordered complete metric-like space. We investigate this new contractive mapping as a generalized weakly contractive mapping in our main results, we display an example and an application to support our obtained results
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