Abstract In this manuscript we introduce the notion of $(\alpha,\beta,\psi,\phi)$ ( ? , ? ? ? ) -interpolative contraction that unifies and generalizes significant concepts: Proinov type contractions, interpo...

In this note we show the somewhat surprising fact that proof of `if part' distinguished characterizations metric completeness due to Kirk, and Suzuki Takahashi, respectively, can be deduced in a straightforward manner from Hu's theorem space is complete if only any Banach contraction on bounded closed subsets thereof has fixed point. We also take advantage approach easily deduce characterizatio...

In this paper, we are concerned with the fractional and higher order H\'{e}non-Hardy type equations \begin{equation*} (-\Delta)^{\frac{\alpha}{2}}u(x)=f(x,u(x)) \,\,\,\,\,\,\,\,\,\,\,\, \text{in} \,\,\, \mathbb{R}^{n}, \mathbb{R}^{n}_{+} \text{or} \Omega \end{equation*} $n>\alpha$, $0<\alpha<2$ or $\alpha=2m$ $1\leq m<\frac{n}{2}$. We first consider typical case $f(x,u)=|x|^{a}u^{p}$ $a\in(-\al...

The fractal interpolation functions with appropriate iterated function systems provide a method to perturb and approximate continuous on compact interval I. This produces class of $$f^{\varvec{\alpha }}\in {\mathcal {C}}(I)$$ , where $$\varvec{\alpha }$$ is vector functional components. presence scaling in these helps get wide variety mappings for approximation problems. current article explore...

A pinnacle of a permutation is value that larger than its immediate neighbors when written in one-line notation. In this paper, we build on previous work characterized admissible sets permutations. For these sets, there can be specific orderings the pinnacles are not admissible, meaning they realized by any permutation. Here characterize orderings, using relationship between x and rank set to b...

In this paper, we consider admissible estimation of the parameter ?r in the gamma distribution with truncated parameter space under entropy loss function. We obtain the classes of admissible estimators. The result can be applied to estimation of parameters in the normal, lognormal, pareto, generalized gamma, generalized Laplace and other distributions.