Related papers: Two fixed point theorems in complete random normed…
In this paper, we give common coincidence point and common fixed point theorems for four self maps in the setting of generalized TAC-contraction in partial b-metric space. Also, we give an example to authenticate the viability of the…
This paper establishes the existence and uniqueness of solutions for rough differential equations driven by reduced rough paths with low regularity, specifically in the roughness regime $\frac{1}{3} < \alpha \leq \frac{1}{2}$. While the…
In this study we provide several significant generalisations of Banach contraction principle where the Lipschitz constant is substituted by real-valued control function that is a comparison function. We study non-stationary variants of…
In this paper, we study the existence of the random approximations and fixed points for random almost lower semicontinuous operators defined on finite dimensional Banach spaces, which in addition, are condensing or 1-set-contractive. Our…
In this paper, we introduce two new types of enriched contractions, viz., enriched $\mathcal{A}$-contraction and enriched $\mathcal{A}'$-contraction. Then we obtain fixed points of mappings satisfying such contractions using the fixed point…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
In the present paper, a new type of mappings called perimetric contractions on $k$-polygons is introduced. These contractions can be viewed as a generalization of mappings that contracts perimeters of triangles. A fixed point theorem for…
We adapt the classical theory of local well-posedness of evolution problems to cases in which the nonlinearity can be accurately quantified by two different norms. For ordinary differential equations, we consider $\dot{x} = f(x,x)$ for a…
In this paper, we prove that the Banach contraction principle proved by S. G. Matthews in 1994 on 0--complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by D. Ili\'{c},…
We augment the dimension of the Euclidean space by one and the Picard iteration of a contraction by a simple iteration on the real line such that the resulting iteration becomes monotone increasing and bounded with respect to the order…
In this article, we introduce a four-point analogue of Banach-type, Kannan-type, and Chatterjea-type contractions, and examine their properties. We establish sufficient conditions under which these mappings achieve fixed points in a…
In this paper we aim to combine tools from variational calculus with modern techniques from quaternionic analysis that involve Dirac type operators and related hypercomplex integral operators. The aim is to develop new methods for showing…
Fixed point theory studies conditions under which nonexpansive maps on Banach spaces have fixed points. This paper examines the open question of whether every reflexive Banach space has the fixed point property. After surveying classical…
A number of landmark existence theorems of nonlinear functional analysis follow in a simple and direct way from the basic separation of convex closed sets in finite dimension via elementary versions of the Knaster-Kuratowski-Mazurkiewicz…
Ever since the proof of asymptotic normality of maximum likelihood estimator by Cramer (1946), it has been understood that a basic technique of the Taylor series expansion suffices for asymptotics of $M$-estimators with…
In this paper, we introduce a generalized notion of monotone property and prove some results regarding existence and uniqueness of multi-tupled fixed points for nonlinear contraction mappings satisfying monotone property in ordered complete…
An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space $X$, there are sufficiently many continuous linear functionals to separate points of $X$. In the paper, we establish a `local'…
In this paper we consider the class of Lipschitz maps on the unit ball $B_X$ of a Banach space $X$, and the question we deal with is whether for any $\lambda>1$ there exists a $\lambda$-Lipschitz fixed-point free mapping $T\colon B_X\to…
We apply methods of the fixed point theory to a Lambda policy iteration with a randomization algorithm for weak contractions mappings. This type of mappings covers a broader range than the strong contractions typically considered in the…
We consider maps defined on the interior of a normal, closed cone in a real Banach space that are nonexpansive with respect to Thompson's metric. With mild compactness assumptions, we prove that the Krasnoselskii iterates of such maps…