Fixed point results under nonlinear Suzuki (F,R≠)-contractions with an application

Abstract

In this article, we introduce the idea of nonlinear Suzuki (F,R?)-contractions, which is patterned after the contractive conditions due to Suzuki [Nonlinear Anal. 71 (2009) 5313-5317] and Wardowski [Fixed Point Theory Appl. (2012) 94:6]. Utilizing our newly introduced contraction, we establish some relation theoretic fixed point theorems. Furthermore, we adopt an example to highlight the genuineness of our newly proved results. Finally, we use our main results to establish the existence and uniqueness of solution for a nonlinear matrix equation.

A Unified Approach and Related Fixed-Point Theorems for Suzuki Contractions

“…Subsequently, many researchers [3][4][5][6][7][8][9][10] further developed this new category by improving its properties and extending it in a more generalized setting. In the meantime, other recently defined concepts such as α-admissible mapping in [11] promoted in [12][13][14][15][16], Suzuki contraction widely used in [17][18][19][20][21], and formulations in partial metric spaces, metric-like spaces, b-metric spaces, and b-metric -like spaces underline their significance and offer a broader understanding in various contexts of the fixed point theory. For an extended introduction, we could mention many new theorems and corresponding classical results with applications in the above spaces, resulting in notions of interpolative and hybrid contractions; see [22][23][24].…”