Some Generalized Fixed Point Results with Applications to Dynamic Programming

Abstract

The aim of this paper is to introduce some generalized contractions and prove certain new fixed point results for self-mappings satisfying these contractions in the setting of F-metric space. As an application of our results, we investigate the problem of dynamic programming related to the multistage process which formulates the problems of computer programming and mathematical optimization. We also provide an example to support the validity of our main results.

Applying fixed point methodologies to solve a class of matrix difference equations for a new class of operators

“…Author details 1 Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi Arabia. 2 Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt. 3 Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt.…”

“…Due to the ease of this principle and its essence, which is related to many applications in various branches of mathematics, many researchers have created various supplements and additions. For example, see [2][3][4][5][6][7][8].…”

“…Numerous academics have discussed the concept of η-contraction, and important theoretical and practical findings have been documented that justify the use of FPs in nonlinear analysis under different spatial constraints. We advise the reader to view [16,17] for further details.…”

On Fixed-Point Results of Generalized Contractions

“…Its results are supportive tools for other fields to solve many problems. Many researchers have put their efforts in obtaining these results; for further study, see [1][2][3][4][5][6][7][8][9][10][11][12] and literature. Because of Banach [4], the Banachcontraction theorem (1922) is indeed the most significant consequence in the theory of fixed points in metric spaces.…”

Iterative Solutions for Solving Variational Inequalities and Fixed-Point Problems

“…At the same time, we are also interested in the fixed-point problem of finding a point u † such that Tu † = u † . Iterative solution for solving a fixed-point problem is an active research field, see, e.g., [16][17][18][19][20][21][22][23][24]. Recently, iterative algorithms for solving variational inequalities and fixed-point problems have been investigated extensively by many authors [25][26][27][28][29][30][31][32][33].…”