In this paper we present integral conductor inequalities connecting the Lorentz p, q-(quasi)norm of a gradient of a function to a one-dimensional integral of the p, q-capacitance of the conductor between two level surfaces of the same function. These inequalities generalize an inequality obtained by the second author in the case of the Sobolev norm. Such conductor inequalities lead to necessary...

Abstract The aim of this work is to establish results in fixed point theory for a pair fuzzy dominated mappings which forms rational V -contraction modular-like metric spaces. Some via partial order and using the graph concept are also developed. We apply our ensure existence solution nonlinear Volterra-type integral equations.

Abstract In this work, we investigate h - ϕ contraction mappings with two metrics endowed a directed graph which involve auxiliary functions. The achievement allows us to obtain applications for the existence of solutions Caputo fractional boundary value problems integral condition type. addition, also give examples and numerical experiments supporting our main results.

In this paper, we introduce the notion of weak $psi$-quasi contraction in generalized metric spaces and using this notion we obtain conditions for the existence of fixed points of a self map in $D$-complete generalized metric spaces. We deduce some corollaries from our result and provide examples in support of our main result.

In this paper, we shall establish error estimates for two important fixed point theorems involving contractive conditions of integral type. Apart from obtaining the error estimates and the rate of convergence for a recent result of Rhoades [18] by imposing an additional condition, a generalization of Berinde [4] is also established in Theorem 2 by introducing a weak contraction condition of int...

Inspired by the fact that the discontinuous mappings cannot be (Banach type) contractions and cyclic contractions need not be continuous, and taking into account that there are applications to integral and differential equations based on cyclic contractions, a new type of cyclic contraction mappings satisfying an implicit relation that involves a control function for a map in a metric space is ...