In this article, we introduce $(\mathrm{\Psi },\mathrm{\Phi })$-orthogonal interpolative contractions which generalize orthogonal interpolative contractions. We investigate different conditions on the functions $\mathrm{\Psi },\mathrm{\Phi }:(0,\mathrm{\infty })\to (-\mathrm{\infty },\mathrm{\infty })$ to show the existence of fixed-points of set-valued $(\mathrm{\Psi },\mathrm{\Phi })$-orthogonal interpolative contractions. Our fixed point results are improvement of several known results in literature. As an application, we resolve a fractional differential equation.

In this paper, we noticed that the existence of fixed points of F-contractions, in $\mathcal{F}$ -metric space, can be ensured without the third condition (F3) imposed on the Wardowski function $F:(0,\infty )\to \mathbb{R}$ . We obtain fixed points as well as common fixed-point results for Reich-type F-contractions for both single and set-valued mappings in $\mathcal{F}$ -metric spaces. To show the usability of our results, we present two examples. Also, an application to functional equations is presented. The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization. Our results extend and generalize the previous results in the existing literature.

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.

We consider some Nemytzki-Edelstein-Meir-Keeler type results in the context of b-metric spaces. In some cases, we assume that the b-metric is continuous. Our results generalize several known ones in existing literature. We also present some examples to illustrate the usability of our results.

In this paper, we manifest some coincidence and common fixed point theorems for four self-mappings satisfying Círíc-type and Hardy–Rogers-type (αs,F)-contractions defined on an αs-complete b-metric space. We apply these results to infer several new and old corresponding results in ordered b-metric spaces and graphic b-metric spaces. Our work generalizes several recent results existing in the literature. We present examples to validate our results. We discuss an application of main result to show the existence of common solution of the system of Volterra type integral equations.

In this paper, we introduce a new set Fsb of nonlinear functions. We obtain unique common fixed point theorems for (β; F)-weak contractions under the effect of functions from Fsb. Moreover, we deduce new common fixed point results in ordered and graphic b-metric spaces. Our work generalizes several recent results existing in the literature. We set up an example to elucidate main result. We apply the main theorem to show the existence of common solution of the system of elliptic boundary value problems.