Best proximity point theorems for α-ψ-proximal contractions in intuitionistic fuzzy metric spaces

Abstract

The aim of this paper is to introduce and study certain new concepts of α-ψ-proximal contractions in an intuitionistic fuzzy metric space. Then we establish certain best proximity point theorems for such proximal contractions in intuitionistic fuzzy metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered intuitionistic fuzzy metric spaces. Several interesting consequences of our obtained results are presented in the form of new fixed point theorems which contain some recent fixed point theorems as special cases. Moreover, we discuss some illustrative examples to highlight the realized improvements. MSC: 47H10; 54H25

Fuzzy Metric Spaces: Optimizing Coincidence and Proximity Points

“…for each  > 0 and . n ∈  Successively apply (24) will leads to ( ) for each m > n > n 0 . It can be inferred that {ω n } is Cauchy.…”

Best Proximity Point Theorems for Cyclic Contractions Mappings in Banach Algebras

“…Regarding the relationship between the noncyclic and cyclic results, the authors in [11] proved that the existence of best proximity points for cyclic nonexpansive mappings is equivalent to the existence of best proximity pairs for noncyclic nonexpansive mappings in the setting of strictly convex Banach spaces. For more on the best proximity point results, the interested reader can consult [12][13][14][15][16][17][18].…”

Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations

“…Thus, a best proximity pair theorem furnishes sufficient conditions for the existence of an optimal approximate solution x, known as a best proximity point of the mapping F, satisfying the condition that d(x, Fx) = d(A, B). Many authors established the existence and convergence of fixed and best proximity points under certain contractive conditions in different metric spaces (see e.g., [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] and references therein).…”