Fixed point of single-valued cyclic weak φF-contraction mappings

Moradi, Sirous

doi:10.2298/fil1409747m

Cited by 9 publications

(5 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If ψ is lower semicontinuous and ϕ is upper semicontinuous, then Theorem 2.4 is an improvement of the Amini-Harandi-Petrusel fixed point theorem [10]. If we take ϕ(y) = h(ψ(y)) in Theorem 2.3, we obtain the following improvement of Moradi's theorem [28].…”

Section: Then T Has a Unique Fixed Point In Amentioning

confidence: 98%

Fixed point problems for generalized contractions with applications

2021

View full text Add to dashboard Cite

In this paper, we investigate the conditions on the control mappings $\psi ,\varphi :(0,\infty )\rightarrow \mathbb{R}$ ψ , φ : ( 0 , ∞ ) → R that guarantee the existence of the fixed points of the mapping $T:X\rightarrow P(X)$ T : X → P ( X ) satisfying the following inequalities: $$ \psi \bigl(H(Tx,Ty)\bigr)\leq \varphi \bigl(d(x,y)\bigr) \quad \forall x,y\in X, \text{provided that } H(Tx,Ty)>0, $$ ψ ( H ( T x , T y ) ) ≤ φ ( d ( x , y ) ) ∀ x , y ∈ X , provided that H ( T x , T y ) > 0 , and $$ \psi \bigl(H(Tx,Ty)\bigr)\leq \varphi \bigl(A(x,y)\bigr) \quad \forall x,y\in X, \text{provided that } H(Tx,Ty)>0, $$ ψ ( H ( T x , T y ) ) ≤ φ ( A ( x , y ) ) ∀ x , y ∈ X , provided that H ( T x , T y ) > 0 , where $A(x,y)=\max \{ d(x,y), d(x,Tx), d(y,Ty), (d(x,Ty) +d(Tx,y))/2 \} $ A ( x , y ) = max { d ( x , y ) , d ( x , T x ) , d ( y , T y ) , ( d ( x , T y ) + d ( T x , y ) ) / 2 } , and $(X, d)$ ( X , d ) is a metric space. The obtained fixed point results improve many earlier results on the set-valued contractions. As an application, we consider the existence of the solutions of an FDE.

show abstract

Section: Then T Has a Unique Fixed Point In Amentioning

confidence: 98%

Fixed point problems for generalized contractions with applications

2021

View full text Add to dashboard Cite

show abstract

“…Defining W(c) = g(V(c)) for all c ∈ (0, ∞) in Theorem 1, we have the following improvement of Moradi's theorem [21].…”

Section: Consequencesmentioning

confidence: 99%

“…He introduced a generalized class of contractions by operating two functions V, W : (0, ∞) → (−∞, ∞) on both sides of the Banach contraction and obtained several fixed point results. The class of contractions given in [19] encapsulate the contractions defined in [4,7,20,21].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Iterative Multivalued ⊥-Preserving Mappings and an Application to Fractional Differential Equation

Nazam

Chandok

Hussain

et al. 2023

Axioms

View full text Add to dashboard Cite

In this paper, we introduce orthogonal multivalued contractions, which are based on the recently introduced notion of orthogonality in the metric spaces. We construct numerous fixed point theorems for these contractions. We show how these fixed point theorems aid in the generalization of a number of recently published findings. Additionally, we offer a theorem that establishes the existence of a fractional differential equation’s solution.

show abstract

“…We receive the following interpolative fractional version of Moradi theorem [30] if we take Φ(J) � h(Ψ(J)) in eorem 2.…”

mentioning

confidence: 99%