Nonexpansive Mappings on New Premodular Special Space of Sequences

For different premodular, which is a generalization of modular, defined by weighted Orlicz sequence space and its prequasi operator ideal, we have examined the existence of a fixed point for both Kannan contraction and nonexpansive mappings acting on these spaces. Some numerous numerical experiments and practical applications are presented to support our results.

Some Fixed Point Results in Premodular Special Space of Sequences and Their Associated Pre-Quasi-Operator Ideal

A weighted Nakano sequence space and the s -numbers it contains are the subject of this article, which explains the concept of the pre-quasi-norm and its operator ideal. We show that both Kannan contraction and nonexpansive mappings acting on these spaces have a fixed point. A slew of numerical experiments back up our findings. The presence of summable equations’ solutions is shown to be useful in a number of ways. Weight and power of the weighted Nakano sequence space are used to define the parameters for this technique, resulting in customizable solutions.

(ρ,η,μ)-Interpolative Kannan Contractions I

We point out a vital error in the paper of Gaba et al. (2019), showing that a (ρ,η,μ) interpolative Kannan contraction in a complete metric space need not have a fixed point. Then we give an appropriate restriction on a (ρ,η,μ)-interpolative Kannan contraction that guarantees the existence of a fixed point and provide an equivalent formulation. Moreover, we show that this formulation can be extended to the interpolative Reich-Rus-Ćirić type contraction.

Some Fixed Point Results of Kannan Maps on the Nakano Sequence Space

In the recent past, some researchers studied some fixed point results on the modular variable exponent sequence space ℓ r . ψ , where ψ v = ∑ a = 0 ∞ 1 / r a v a r a and r a ≥ 1 . They depended on their proof that the modular ψ has the Fatou property. But we have explained that this result is incorrect. Hence, in this paper, the concept of the premodular, which generalizes the modular, on the Nakano sequence space such as its variable exponent in 1 , ∞ and the operator ideal constructed by this sequence space and s -numbers is introduced. We construct the existence of a fixed point of Kannan contraction mapping and Kannan nonexpansive mapping acting on this space. It is interesting that several numerical experiments are presented to illustrate our results. Additionally, some successful applications to the existence of solutions of summable equations are introduced. The novelty lies in the fact that our main results have improved some well-known theorems before, which concerned the variable exponent in the aforementioned space.

Kannan Contraction Operator on the Domain of r . -Cesàro Matrix in ℓ t . and Related Prequasi Ideal with an Application of Nonlinear Difference Equations

In this article, the sequence space Ξ r , t υ has been built by the domain of r l -Cesàro matrix in Nakano sequence space ℓ t l , where t = t l and r = r l are sequences of positive reals with 1 ≤ t l < ∞ , and υ f = ∑ l = 0 ∞ ∑ z = 0 l r z f z / ∑ z = 0 l r z t l , with f = f z ∈ Ξ r , t . Some topological and geometric behavior of Ξ r , t υ , the multiplication maps acting on Ξ r , t υ , and the eigenvalues distribution of operator ideal constructed by Ξ r , t υ and s -numbers have been examined. The existence of a fixed point of Kannan prequasi norm contraction mapping on this sequence space and on its prequasi operator ideal are investigated. Moreover, we indicate our results by some explanative examples and actions to the existence of solutions of nonlinear difference equations.

A discussion on the coincidence quasi-best proximity points

In this paper, we first introduce a new class of the pointwise cyclic-noncyclic proximal contraction pairs. Then we consider the coincidence quasi-best proximity point problem for this class. Finally, we study the coincidence quasi-best proximity points of weak cyclic-noncyclic Kannan contraction pairs. We consider an example to indicate the validity of the main result.

Some Remarks on Fixed Point Theorems for Interpolative Kannan Contraction

In this paper, we use interpolation to obtain fixedpoint and common fixed point results for a new type of Kannan contraction mappings in complete metric and b -metric spaces. Our results extend and improve some results on fixed point theory in the literature. We also give some examples to illustrate the given results.

A fixed point theorem of Kannan type that characterizes fuzzy metric completeness

We obtain a fixed point theorem for complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends the classical Kannan fixed point theorem. We also show that, in fact, our theorem allows to characterize the fuzzy metric completeness, extending in this way the well-known Reich-Subrahmanyam theorem that a metric space is complete if and only if every Kannan contraction on it has a fixed point.

On Fixed-Point Results in Controlled Partial Metric Type Spaces with a Graph

Recently, Mlaiki et al. introduced the notion of a controlled metric type space which is a generalization of the b-metric space. In this work, we define the controlled partial metric type space and give some fixed-point theorems for extensions of Kannan contraction in this space with suitable conditions. Moreover, as an application, we derive a fixed-point theorem for graphic contraction on the considered metric space endowed with a graph.