On the Correlation between Banach Contraction Principle and Caristi’s Fixed Point Theorem in b-Metric Spaces

Abstract

We solve a question posed by E. Karapinar, F. Khojasteh and Z.D. Mitrović in their paper “A Proposal for Revisiting Banach and Caristi Type Theorems in b-Metric Spaces”. We also characterize the completeness of b-metric spaces with the help of a variant of the contractivity condition introduced by the authors in the aforementioned article.

Common Fixed Point of (ψ, β, L)-Generalized Contractive Mapping in Partially Ordered b-Metric Spaces

“…Otherwise, for more notions such as b-convergence, b-completeness, b-Cauchy sequence and b-continuity in b-metric spaces, the reader may refer to [1,[4][5][6][7][8][9][10][11]13,[15][16][17][18][19][20][21][22][23][24][25][26][27][28] and the references mentioned therein.…”

The Generalization of Ciric and Caristi Type Fixed Point Theorem

“…And the most remarkable form is Caristi [6,7] type fixed point theorem based on Banach Contraction Principle. Since Caristi type fixed point theorem equals to Ekeland 􀆳 s variational principle [8,9] , it has various applications in nonlinear analysis and variational inequalities [10][11][12][13] .…”