Generalizations of some contractions in b-metric-like spaces and applications to boundary value problems

Abstract

This paper provides two wide classes of contractions, which are obtained by using notions of $\alpha _{s^{p}} $ α s p -admissibility and the rich set of C-class functions in the setting of a complete b-metric-like space under more general contractive conditions. An application is provided and many known results in the literature can be derived.

General New Results on (ϕ,F)−Contractions in b−Metric-like-Spaces

“…We emphasize some of the maingeneralizations that provide great developments to the fixed point theory, such as the concepts of b−metric [2,3] and b−metric-like [4]; many scientists have contributed to this theory with papers and essential results, and furthermore we can list references [5][6][7][8][9][10][11][12][13][14]. In 2012, Samet defined α−admissible mapping [15], and further triangular α−admissible mapping [16].…”