Abstract
We consider a fixed-point problem for mappings involving a rational type and almost type contraction on complete metric spaces. To do this, we are using F -contraction and H , φ -contraction. We also present an example to illustrate our result.
Highlights
The beginning of metrical fixed point theory is related to Banach’s Contraction Principle, presented in 1922 [1], which says that any contraction self-map on M has a unique fixed point whenever ðM, dÞ is complete
If fμng is a sequence of Picard starting at μ0 ∈ M, lim n→+∞
We show that fμng is a Cauchy
Summary
The beginning of metrical fixed point theory is related to Banach’s Contraction Principle, presented in 1922 [1], which says that any contraction self-map on M has a unique fixed point whenever ðM, dÞ is complete. The mapping Y is called an F H-contraction if there exists F ∈ F, H ∈ H , a real number, τ > 0 and φ : M → 0,+∞Þ s.t. τ + FðHðdðYμ, YγÞ, φðYμÞ, φðYγÞÞÞ ≤ FðHðdðμ, γÞ, φðμÞ, φðγÞÞÞ, ð8Þ
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