New approach of Lebesgue integral in revised fuzzy cone metric spaces via unique coupled fixed point theorems

Abstract

Introduction/purpose: This article introduces the concept of revised fuzzy cone contraction by using the concept of a traiangular conorm and Revised Fuzzy Cone contractive conditions. Methods: This article established new Revised Fuzzy Cone Contraction (RFC-C) type unique coupled Fixed Point theorems (FP theorems) in revised fuzzy cone metric spaces (RFCMS) by using the triangular property of RFCMS. Results: The obtained results on fixed points in revised fuzzy cone metric spaces generalize some known results in the litrature and present illustrative examples to support the main work. Conclusion: The RFC contractive conditions generalize some important contraction types and examine the existence of a fixed point in revised fuzzy cone metric spaces. In addition, the Lebesgue integral type mapping is applied to get the existence result of a unique coupled fixed point in RFCMS to validate the main work.

Keywords

• revised fuzzy metric
• revised fuzzy cone
• fixed point