Generalized contraction theorems approach to fuzzy differential equations in fuzzy metric spaces

• DOI: 10.3934/math.2022628
• Publication Date: 2022-04-11T10:34:16Z
• Authors: Iqra Shamas; Saif Ur Rehman; Thabet Abdeljawad; Mariyam Sattar; Sami Ullah Khan; Nabil Mlaiki
• Keywords: Artificial intelligence; Contraction mapping; Mathematical analysis; 01 natural sciences; Fixed Point Theorems in Metric Spaces; contraction conditions; QA1-939; FOS: Mathematics; fuzzy metric space; 0101 mathematics; Fixed-point theorem; Internal medicine; Fixed Point Theorems; Pure mathematics; common fixed point; Discrete mathematics; Generalized Contractions; Applied mathematics; Computer science; Fuzzy logic; fixed point; fuzzy differential equations; Physical Sciences; Contraction (grammar); Medicine; Geometry and Topology; Fuzzy Metric Spaces; Metric space; Mathematics

<abstract><p>Fixed point theory is one of the most interesting areas of research in mathematics. In this direction, we study some unique common fixed point results for a pair of self-mappings without continuity on fuzzy metric spaces under the generalized contraction conditions by using "the triangular property of fuzzy metric". Moreover, we present weak-contraction and generalized Ćirić-contraction theorems. The results are supported by suitable examples. Further, we establish a supportable application of the fuzzy differential equations to ensure the existence of a unique common solution to validate our main work.</p></abstract>