Semi-metric spaces and fixed points of α−φ -contractive maps

Abstract

A negative answer to an open problem is provided. Fixed point results for α-ϕ-contractive mappings in semi-metric spaces are proved. To show the generality of our results, examples are given. Finally, an application of our result to probabilistic spaces is derived.

ON H+Type Multivalued Contractions and Applications in Symmetric and Probabilistic Spaces

“…If we replace multivalued mappings by single valued mappings in all of the above results, then we get corresponding results for the single valued mappings as corollaries. The main results in [48] are corollaries to Theorems 1 and 3 for single valued mappings. Let us define α :…”

“…Very recently in [48], fixed point results for single valued α-ϕ-contractive mappings in symmetric spaces are obtained.…”

A Common Fixed Point Theorem for Nonlinear Quasi-Contractions on b -Metric Spaces with Application in Integral Equations

“…In [26], the authors give examples for the following relationships: ðW3Þ⇒ðW4Þ, ðW4Þ⇒ðHEÞ, ðW4Þ⇒ðCCÞ, ðW3Þ ⇒ðHEÞ, ðW3Þ⇒ðCCÞ, ðCCÞ⇒ðW4Þ, ðHEÞ⇒ðCCÞ, ðHEÞ⇒ ðW3Þ, ðHEÞ⇒ðW4Þ, and ðCCÞ⇒ðHEÞ. The fact that ðWÞ ⇒ðCCÞ has been proved in [27]. Definition 1.…”

Some New Types of α_(β^(-1) )-admissible Mappings and Fixed Point Results

“…Almost researchers in this direction have used 𝛼-admissible condition. For example see [8], [9], [10], [11], [12], [13], [14], [15].…”