Fixed Point Theory in -Complete Metric Spaces with Applications

By Nawab Hussain, Marwan Amin Kutbi, Peyman Salimi. 2014

123 citations recorded by the source corpus.

The aim of this paper is to introduce new concepts of --complete metric space and --continuous function and establish fixed point results for modified ---rational contraction mappings in --complete metric spaces. As an application, we derive some Suzuki type fixed point theorems and new fixed point theorems for -graphic-rational contractions. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/631c88995346132b91deea8bc55ce1dafc54f0f9

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In Geometry and Topology

Citations in the corpus

Notes on Some Recent Papers Concerning $F$-Contractions in $b$-Metric Spaces (2018, background): “(1) [7] The space (X, b, s) is calledα-complete if every Cauchy sequence {xn} inX withα(xn, xn+1) ≥ 1 for all n ∈ N converges in X .”
ON H+Type Multivalued Contractions and Applications in Symmetric and Probabilistic Spaces (2019, background): “[45] (see also [46]) weakens the metric completeness.”
SUZUKI-WARDOWSKI TYPE FIXED POINT THEOREMS FOR $\alpha$-GF-CONTRACTIONS (2014, background): “This result has been extended in many directions (see [1-18]).”