On Solution of Boundary Value Problems via Weak Contractions

The aim is to present a new relational variant of fixed point result that generalizes various fixed point results of the existing theme for contractive type mappings. As an application, we solve a periodic boundary value problem and validate all assertions with the help of nontrivial examples. We also highlight the close connections of the fixed point results equipped with a binary relation to that of graph related metrical fixed point results. Radically, these investigations unify the theory of metrical fixed points for contractive type mappings.

A Multiple Fixed Point Result for θ , ϕ , ψ -Type Contractions in the Partially Ordered s -Distance Spaces with an Application

In this manuscript, the aim is to prove a multiple fixed point (FP) result for partially ordered s -distance spaces under θ , ϕ , ψ -type weak contractive condition. The result will generalize some well-known results in literature such as coupled FP (Guo and Lakshmikantham, 1987), triple fixed point (Berinde and Borcut, 2011), and quadruple FP results (Karapinar, 2011). Moreover, to validate the result, an application for the existence of solution of a system of integral equations is also provided.

Near-Common Fixed Point Result in Cone Interval b-Metric Spaces over Banach Algebras

In this article, we proposed the concept of cone interval b-metric space over Banach algebras. Furthermore, some near-fixed point and near-common fixed point results are proved in the context of cone interval b-metric space and normed interval spaces for self-mappings under different types of generalized contractions. An example is presented to validate our main outcome.

Symmetric Spaces Approach to Various Cyclic Contractions and Application to Probabilistic Spaces

This paper aims to prove fixed point results for cyclic compatible contraction and Hardy–Rogers cyclic contraction in symmetric spaces. Our results generalize the results of Kumari and Panthi (2016) proved for cyclic compatible contraction and modified Hardy–Rogers cyclic contraction in the generating space of a b-quasi metric family and b-dislocated metric family. After that, as an application, we prove a fixed point result in symmetric pre-probabilistic metric spaces (PPM-spaces).

A solution to nonlinear Fredholm integral equations in the context of w-distances

In this paper we propose a solution to the nonlinear Fredholm integral equations in the context of w-distance. For this purpose, we also provide a fixed point result in the same setting. In addition, we provide best proximity point results. We give examples and present numerical results to approximate fixed points.

On the Nielsen root theory of n-valued maps

Let $$\phi :X \multimap Y$$ ϕ : X ⊸ Y be an n-valued map of connected finite polyhedra and let $$a \in Y$$ a ∈ Y . Then, $$x \in X$$ x ∈ X is a root of $$\phi $$ ϕ at a if $$a \in \phi (x)$$ a ∈ ϕ ( x ) . The Nielsen root number $$N(\phi : a)$$ N ( ϕ : a ) is a lower bound for the number of roots at a of any n-valued map homotopic to $$\phi $$ ϕ . We prove that if X and Y are compact, connected triangulated manifolds without boundary, of the same dimension, then given $$\epsilon > 0$$ ϵ > 0 , there is an n-valued map $$\psi $$ ψ homotopic to $$\phi $$ ϕ within Hausdorff distance $$\epsilon $$ ϵ of $$\phi $$ ϕ such that $$\psi $$ ψ has finitely many roots at a. We conjecture that if X and Y are q-manifolds without boundary, $$q \ne 2$$ q ≠ 2 , then there is an n-valued map homotopic to $$\phi $$ ϕ that has $$N(\phi : a)$$ N ( ϕ : a ) roots at a. We verify the conjecture when $$X = Y$$ X = Y is a Lie group by employing a fixed point result of Schirmer. As an application, we calculate the Nielsen root numbers of linear n-valued maps of tori.

Fixed point theorems via Generalized WF-Contractions with applications

The aim of this paper is to introduce a new class of mixed contractions which allow to revise and generalize some results obtained in [6] by R. Gubran, W. M. Alfaqih and M. Imdad. We also provide an example corresponding to this class of mappings and show how the new fixed point result relates to the above-mentioned result in [6]. Further, we present an application to the solvability of a two-point boundary value problem for second order differential equations.

On Two Banach-Type Fixed Points in Bipolar Metric Spaces

In this article, we propose two Banach-type fixed point theorems on bipolar metric spaces. More specifically, we look at covariant maps between bipolar metric spaces and consider iterates of the map involved. We also propose a generalization of the Banach fixed point result via Caristi-type arguments.

On Fixed Point Result in Double Controlled Metric Spaces

In this paper, we introduce Hardy and Rogers type contractions in the class of double controlled metric spaces and establish fixed point theorem. Our result are generalization of some known results of literature. We also provide example to illustrate significance of the established result .