Fixed point problems concerning contractive type operators on KST-Spaces

Ansari, Arslan H., Guran, Liliana and Latif, Abdul

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Issue no: Vol 34/2018 no. 3 Tags: Fixed point, Well-posedness, $\alpha$-$\psi$-weakly contractive operator, $KST$-space, Ulam-Hyers $w$-stability

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In this paper, using the concept of $w$ -distance we prove some results on the existence of fixed points for contractive type
operators, namely; $(\alpha,\mu)$ – $\psi$ -contractive operators. Applications are also presented. Our results improve and
generalize a number of known results of fixed point theory including the recent results of Guran and Bota [Guran, L. and Bota, M.-F. Ulam-Hyers Stability Problems for Fixed Point Theorems concerning $\alpha$ – $\psi$ -Type Contractive
Operators on $KST$ -Spaces, Submitted in press] and Ansari [Ansari, A. H. and Shukla, S., Some fixed point theorems
for ordered $F$ – $(\mathcal{F},h)$ -contraction and subcontractions in $\theta$ – $f$ -orbitally complete partial metric spaces, J. Adv. Math. Stud., 9 (2016), No. 1, 37–53].