A well-quasi-order is an order which contains no infinite decreasing sequence and no infinite collection of incomparable elements. In this paper, we consider graph classes defined by excluding one graph as contraction. More precisely, we give a complete characterization of graphs H such that the class of H-contraction-free graphs is well-quasi-ordered by the contraction relation. This result is...

In this paper we present fuzzy coupled fixed point results in the turf of complete b-metric spaces via nonlinear F-contraction; follow derive some interesting as byproducts. Eventually, apply our solving Volterra integral equations and Caputo-Hadamard type fractional differential equations.

In this paper, we define \(\theta\)-\(\phi\)-contraction on a \(b\)-metric space into itself by extending \(\theta\)-\(\phi \)-contraction introduced Zheng {et al.} [D. W. Zheng, Z. Y. Cai, P. Wang, J. Nonlinear Sci. Appl., \(\bf 10\) (2017), 2662--2670] in metric and also, prove \(\theta \)-type theorem the setting of spaces as well framework \(b\)-rectangular spaces. Moreover, give some appli...

In this paper, we obtain the existence of unique solution anti-periodic type (anti-symmetry) integral multi-point boundary conditions for sequential fractional differential equations. We apply Banach contraction mapping principle to get desired results. Our results specialize and extend some existing

In this paper existence and uniqueness of fixed points are proved for self maps, satisfying a new contraction without assuming the compatibility commutative property maps. Some remarks applications to integral type given illustrate importance our results. An open problem future research is also given.