We generalize various types of F -contractions defined by Wardowski, Vetro and others to b-metric spaces prove fixed point theorems for them.The examples given show that these generalizations extend the existing results in a significant way.

Abstract We present a generic functional inequality on Riemannian manifolds, both in additive and multiplicative forms, that produces well known genuinely new Hardy-type inequalities. For the version, we introduce Riccati pairs extend Bessel developed by Ghoussoub Moradifam ( Proc. Natl. Acad. Sci. USA , 2008 & Math. Ann. 2011). This concept enables us to give very short/elegant proofs of number celebrated inequalities manifolds with sectional curvature bounded from above simply solving...

In this paper we correct an inaccuracy that appears in the proof of Theorem 1. Czerwik's article "Contraction mappings $b$-metric spaces.", Acta Math. Inform. Univ. Ostraviensis, 1:5--11, 1993.

The goal of this paper is to provide sharp spectral gap estimates for problems involving higher-order operators (including both the clamped and buckling plate problems) on Cartan–Hadamard manifolds. proofs are symmetrization-free — thus no isoperimetric inequality needed based two general, yet elementary functional inequalities. estimate plates solves a asymptotic problem from [Q.-M. Cheng H. Yang, Universal inequalities eigenvalues hyperbolic space, Proc. Amer. Math. Soc. 139(2) (2011)...

We present a generic functional inequality on Riemannian manifolds, both in additive and multiplicative forms, that produces well known genuinely new Hardy-type inequalities. For the version, we introduce Riccati pairs extend Bessel developed by Ghoussoub Moradifam (Proc. Natl. Acad. Sci. USA, 2008 & Math.A nn., 2011). This concept enables us to give very short/elegant proofs of number celebrated inequalities manifolds with sectional curvature bounded from above simply solving Riccati-type...

The goal of this paper is to provide sharp spectral gap estimates for problems involving higher-order operators (including both the clamped and buckling plate problems) on Cartan-Hadamard manifolds. proofs are symmetrization-free -- thus no isoperimetric inequality needed based two general, yet elementary functional inequalities. estimate plates solves a asymptotic problem from Cheng Yang [Proc. Amer. Math. Soc., 2011] concerning behavior eigenvalues hyperbolic spaces, answers question...

In this paper we characterize the sequentially weakly lower semicontinuity of parameter-depending energy functional associated with critical Kirchhoff problem in context (sub)Riemannian manifolds. We also present some spectral gap and convexity results.

We present a simple method for proving Rellich inequalities on Riemannian manifolds with constant, non-positive sectional curvature. The is built upon convexity arguments, integration by parts, and the so-called Riccati pairs, which are based solvability of Riccati-type ordinary differential inequality. These results can be viewed as higher order counterparts recent work Kaj\'ant\'o, Krist\'aly, Peter, Zhao, discussing Hardy using pairs.

In this paper we investigate the Riemannian extensibility of saturation phenomena treated first in Euclidean framework by Brandolini et al. [Sharp estimates and for a nonlocal eigenvalue problem. Adv Math (N Y). 2011;228(4):2352–2365.]. The problem is formulated terms perturbation Laplace-Beltrami operator integral unknown function: increases with weight affecting up to finite critical value then remains constant, i.e. it saturates. Given manifold certain curvature constraints, using...

"This paper investigates whether some fixed point theorems for quasicontractions on metric spaces introduced by Ciric in [1] and generalised Kumam et al. [2] can be improved further. It turns out that the answer is negative. We provide two examples of complete operators without points. prove any possible straightforward relaxation quasi-contractive conditions, one these satisfies condition."

This paper investigates whether some fixed point theorems for quasi-contractions on metric spaces introduced by \`Cir\`ic in [1] and generalised Kumam et al. [2] can be improved further. It turns out that the answer is negative. We provide two examples of complete operators without points. prove any possible straightforward relaxation quasi-contractive conditions, one these satisfies condition.