Ozgur Ege

Jan 3, 2024 | mdpi.com | Arul Joseph Gnanaprakasam |Balaji Ramalingam |Gunaseelan Mani |Ozgur Ege

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Sep 27, 2023 | mdpi.com | Balaji Ramalingam |Ozgur Ege |Ahmad Aloqaily |Nabil Mlaiki

Share and CiteMDPI and ACS StyleRamalingam, B.; Ege, O.; Aloqaily, A.; Mlaiki, N. Fixed-Point Theorems on Fuzzy Bipolar b-Metric Spaces. Symmetry 2023, 15, 1831. https://doi.org/10.3390/sym15101831AMA StyleRamalingam B, Ege O, Aloqaily A, Mlaiki N. Fixed-Point Theorems on Fuzzy Bipolar b-Metric Spaces. Symmetry. 2023; 15(10):1831. https://doi.org/10.3390/sym15101831Chicago/Turabian StyleRamalingam, Balaji, Ozgur Ege, Ahmad Aloqaily, and Nabil Mlaiki. 2023.

Apr 19, 2023 | mdpi.com | Gunaseelan Mani |Arul Joseph Gnanaprakasam |Santosh Kumar |Ozgur Ege

Let η0∈Θ and σ0∈Ψ. Then, Π(ηα)=σα and Π(σα)=ηα+1 for all α∈N∪{0}. Therefore, ({ηα},{σα}) is a bisequence on FCBMS (Θ,Ψ,Γb,∗). Now,Γb(η1,σ0,ℵ)=Γb(Π(σ0),Π(η0),ℵ)≥Γb(η0,σ0,ℵh),for all ℵ>0 and α∈N. Then,Γb(ηα,σα,ℵ)=Γb(Π(σα−1),Π(ηα),ℵ)≥Γb(η0,σ0,ℵh2α)(7)andΓb(ηα+1,σα,ℵ)=Γb(Π(σα),Π(ηα),ℵ)≥Γb(η0,σ0,ℵh2α+1),(8)for all ℵ>0 and α∈N. Let α<β∈N.