Abstract
A picture fuzzy n-normed linear space (NPF), a mixture of a picture fuzzy set and an n-normed linear space, is a proficient concept to cope with uncertain and unpredictable real-life problems. The purpose of this manuscript is to present some novel contractive conditions based on NPF. By using these contractive conditions, we explore some fixed point theorems in a picture fuzzy n-Banach space (BPF). The discussed modified results are more general than those in the existing literature which are based on an intuitionistic fuzzy n-Banach space (BIF) and a fuzzy n-Banach space. To express the reliability and effectiveness of the main results, we present several examples to support our main theorems.
Highlights
In various real-life problems, for a suitable mapping, the existence of a solution and existence of a fixed point (FP) are equivalent
The extensive useful techniques capable with both algebraic and topological properties are those of a normed linear space (NLS), but the continuous maps are more proficient in the sense of NLS
We present some novel contractive conditions based on NPF. By using these contractive conditions, we instigate some fixed point theorems for a picture fuzzy n-Banach space (BPF)
Summary
In various real-life problems, for a suitable mapping, the existence of a solution and existence of a fixed point (FP) are equivalent. Journal of Function Spaces (2) By using these contractive conditions, some fixed point theorems are explored for a picture fuzzy n-Banach space (BPF) These results are more modified and more general than the existing results which are based on an intuitionistic fuzzy n-Banach space (BIF) and a fuzzy n-Banach space (3) To express the reliability and effectiveness of the explored approaches, we explain examples in support of the main results. The rest of this manuscript is summarized in the following ways: In Section 2, we review some basic notions like NIF and their related properties used in the presented work.
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