Symmetrical Hybrid Coupled Fuzzy Fixed-Point Results on Closed Ball in Fuzzy Metric Space with Applications

Abstract

In this research, we establish some new fixed-point results for a symmetric coupled dominated fuzzy mapping satisfying a new advanced contraction on a closed ball in the setting of complete fuzzy metric spaces. In addition, the new notion of hybrid fuzzy-graph-dominated mappings introduced in fuzzy metric spaces achieves some new advanced fuzzy fixed-point problems. Some new definitions and illustrative examples are given to validate our new findings. Lastly, to demonstrate the originality of our new results, we present an application to the Fredholm-type integral equation.

Application to fixed point theory of α-θ-E-Geraghty Pata proximal contractions

“…Numerous publications [20][21][22] investigated fixed point results of various forms, including single, coupled, tripled, and others. Using the mixed monotone property, Bhaskar, Lakshmikantham [15], in 2006, proved some results of coupled fixed point.…”

On some fixed point results using CG simulation functions via w-distance with applications

“…In the realm of metric fixed points, Banach pioneered the renowned Banach's contraction principle [1] , a cornerstone method pivotal for establishing the existence and uniqueness of solutions to a multitude of problems in mathematical analysis. Subsequently, a plethora of researchers have contributed by extending and enhancing the Banach contraction principle in diverse directions and spaces, as exemplified in works such as [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] . Subsequently, Kada et al [15] delved into the realm of metric spaces, introducing the concept of w -distance mappings and establishing significant fixed-point results.…”