Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces

Abstract

The main purpose of this article is to discuss the existence of the common solution of second-order nonlinear boundary value problems        x ′′ (ȷ) = k(ȷ, x(ȷ), x ′ (ȷ)), if ȷ ∈ [0, Λ], Λ > 0, x(ȷ 1) = x 1 , x(ȷ 2) = x 2 , ȷ 1 , ȷ 2 ∈ [0, Λ], (0.1) where k : [0, Λ] × S(S) × S(S) → S(S) is a continuous function and S(S) is a family of fuzzy sets. In this regard we obtain common fixed point results for two pairs of fuzzy mappings satisfying rational contractive condition in the setting of complex valued metric spaces. Our results improve those reported in the existing literature.

Contraction Mappings in Intuitionistic Fuzzy Rectangular Extended B-Metric Spaces

“…Since (V, M, N, * , ○) is a complete IFREBMS for the sequence 8 n 􏼈 􏼉, writing σ � σ/3 + σ/3 + σ/3 and using the rectangular inequality given in ( 5) and (10) on M(8 n , 8 n+p , σ) and N(8 n , 8 n+p , σ) in the following cases.…”

“…Since (V, M, N, * , ○) is a complete IFREBMS for the sequence 8 n 􏼈 􏼉, write σ � σ/3 + σ/3 + σ/3 and use the rectangular inequalities given in ( 5) and (10)…”

“…Mehmood et al [9] presented the concept of fuzzy rectangular metric spaces and fuzzy rectangular b-metric spaces (FRBMSs) and proved Banach contraction principle in the sense of FRBMSs. Hezarjaribi [10] originated the idea of orthogonal FMSs and proved various xed-point results. Authors, in [11][12][13][14], are proved several xed-point results for contraction mappings in FMSs.…”

Some fixed point theorems on complex valued modular metric spaces with an application

“…Then, this space has been studied by many authors. After that, they obtained various …xed point theorems on this spaces [2,7,15,16,22,24,31,32,33,34]. On the other hand, a lot of researchers have contributed introducing di¤erent concepts on these structures.…”