Double Controlled Partial Metric Type Spaces and Convergence Results

Abstract

In this paper, we firstly propose the notion of double controlled partial metric type spaces, which is a generalization of controlled metric type spaces, partial metric spaces, and double controlled metric type spaces. Secondly, our aim is to study the existence of fixed points for Kannan type contractions in the context of double controlled partial metric type spaces. The proposed results enrich, theorize, and sharpen a multitude of pioneer results in the context of metric fixed point theory. Additionally, we provide numerical examples to illustrate the essence of our obtained theoretical results.

\'C}iri{\'c} Contraction with Graphical Structure of Bipolar Metric Spaces and Related Fixed Point Theorems

“…{(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (1,2), (1,3), (1,4), (1,5), (1,6), (1,7), (2,3), (2,4), (2,5), (2,6), (2,7), (3,4), (3,5), (3,6), (3,7), (4,5), (4,6), (4, 7), (5,6), (5,7), (6, 7) Hence, we conclude that graphical bipolar metric space is not necessarily bipolar metric space. Now, we discuss Cauchy, complete, covariant and contravariant mappings as follows:…”

“…In the literature of fixed point theory, the Banach contraction principle is very significant. Many authors have generalized this concept by utilizing various kinds of contraction mappings in several metric spaces (see, e.g., [1,3,5,12,13,21,25]). In 2016, Mutlu and Gürdal [14] introduced the notion of bipolar metric space, a sort of partial distance, as well as the relationship between metric spaces and bipolar metric spaces.…”

Making Decisions about How to Solve Nonlinear Dynamical Systems of the Kannan Type in a New Complex Function Space of Formal Power Series

“…Te nonlinear analysis places signifcant weight on the Banach contraction principle (BCP), a potent instrument for nonlinear analysis. For more interesting articles on various real-world applications of the BCP, see the following: Diening et al [2] discussed Lebesgue and Sobolev spaces with variable exponents, Ruẑiĉka [3] gave a mathematical description of electrorheological fuids, the types of approaches to impartial probabilistic functional diferential equations that are motivated by pure leaps were described by Mao et al [4], Younis et al [5] presented generalized contractions, Guo and Zhu [6] investigated the fxed point approach of stochastic Volterra-Levin equations with Poisson jumps, Ahmad et al [7] provided dual partial metric type spaces, as well as converging fndings, Beg [8] applied FPT to ordered uniform convexity in ordered convex metric spaces, Yang and Zhu [9] examined the kind of solutions to stochastic neutral functional diferential equations of Sobolev-type, and Beg et al [10] discussed about the polytopic fuzzy sets to multiple-attribute decision-making problems. For more interesting articles on diferent real-world applications of fractional calculus, see the following: Rezapour et al [11] discussed a mathematical analysis of a system of Caputo-Fabrizio fractional diferential equations for the anthrax disease model in animals, Mohammadi et al [12] investigated a theoretical study of the Caputo-Fabrizio fractional modeling for hearing loss due to the Mumps virus with optimal control, Khan et al [13] suggested a case study of a fractal-fractional tuberculosis model in China: existence and stability theories along with numerical simulations, Etemad et al [14] studied some novel mathematical analyses on the fractal-fractional model of the AH1N1/09 virus and its generalized Caputo-type version, Matar et al [15] proposed using generalized Caputo fractional derivatives to investigate the p-Laplacian nonperiodic nonlinear boundary value problem, Baleanu et al [16] gave a new study on the mathematical modeling of the human liver with Caputo-Fabrizio fractional derivative, Tuan et al [17] presented a mathematical model for COVID-19 transmission by using the Caputo fractional derivative, Baleanu et al [18] used a new fractional derivative approach to analyze the model of HIV-1 infection of CD4 + T-cells, and Kannan [19] illustrated a new category of discontinuous contraction operators.…”

Decision-Making on the Solution of a Stochastic Nonlinear Dynamical System of Kannan-Type in New Sequence Space of Soft Functions

“…But there are drawbacks to these theories that must be considered. For more information and real-world examples, please refer to [1][2][3][4][5][6][7][8][9][10]. Numerous mathematicians have investigated potential expansions to the theorem and its applications in various contexts since the publication of the book [11] on the Banach fixed point theorem.…”