Abstract In this paper we study fractional initial value problems with Caputo–Fabrizio derivative which involves nonsingular kernel. First apply α - ℓ -contraction and -type F mappings to the existence uniqueness of solutions for such problems. Finally, use some contraction in complete $\mathfrak{F}$ F -metri...

In this paper, we have established and proved fixed point theorems for the Boyd-Wong-type contraction in metric spaces. particular, generalized existing results a pair of mappings that possess but not continuous at point. We can apply result both discontinuous mappings. concluded our by providing an illustrative example each case application to existence uniqueness solution nonlinear Volterra i...

best approximation results provide an approximate solution to the fixed point equation $tx=x$, when the non-self mapping $t$ has no fixed point. in particular, a well-known best approximation theorem, due to fan cite{5}, asserts that if $k$ is a nonempty compact convex subset of a hausdorff locally convex topological vector space $e$ and $t:krightarrow e$ is a continuous mapping, then there exi...

In this article, we introduce a new concept of admissible contraction and prove fixed point theorems which generalize Banach principle in different way more than the known results from literature. The article includes an example shows validity our results, additionally obtain solution integral equation by mapping setting b-metric spaces.

In this paper, we introduce a new class of mappings called “generalized β-ϕ-Geraghty contraction-type mappings”. We use our to formulate and prove some coupled fixed points in the setting partially ordered metric spaces. Our results generalize unite several findings known literature. also provide examples support illustrate theoretical results. Furthermore, apply discuss existence uniqueness so...

In this paper, we modify the KF-iteration process into hyperbolic metric spaces where symmetry condition is satisfied and establish weak w2-stability data dependence results for contraction mappings. We also prove some Δ-convergence strong convergence theorems generalized (α,β)-nonexpansive type 1 Finally, offer a numerical example of mappings show that more effective than other iterations. Our...

In this paper, we extend a multi-valued contraction mapping to a cyclic multi-valued contraction mapping. We also establish the existence of common fixed point theorem for a cyclic multi-valued contraction mapping. Our results extend, generalize and unify Nadler’s multi-valued contraction mapping and many fixed point theorems for multivalued mappings. © 2012 Elsevier Ltd. All rights reserved.