‎In this paper‎, ‎we introduce more general contractions called $varphi $-fixed‎ ‎point point for $(F,varphi‎ ,‎alpha )_{s}$ and $(F,varphi‎ ,‎alpha )_{s}$-‎weak contractions‎. ‎We prove the existence and uniqueness of $varphi $-‎fixed point point for $(F,varphi‎ ,‎alpha )_{s}$ and $(F,varphi‎ ,‎alpha‎‎)_{s}$-weak contractions in complete $b$-metric spaces‎. ‎Some examples are‎ ‎supplied to sup...

Abstract We prove that for any semi-norm $\|\cdot \|$ on $\mathbb{R}^n$ and symmetric convex body $K$ in $\mathbb{R}^n,$(1)$$\begin{align}& \int_{\partial K} \frac{\|n_x\|^2}{\langle x,n_x\rangle}\leq \frac{1}{|K|}\left(\int_{\partial \|n_x\| \right)^2, \end{align}$$and characterize the equality cases of this new inequality. The above would also follow from Log-Brunn–Minkowski conjecture if...

The articles [20], [21], [6], [7], [22], [8], [3], [1], [4], [14], [13], [19], [16], [9], [2], [5], [10], [17], [11], [18], [12], and [15] provide the notation and terminology for this paper. Let f be a partial function from C to C. The functor <(f) yielding a partial function from C to R is defined as follows: (Def. 1) dom f = dom<(f) and for every complex number z such that z ∈ dom<(f) holds ...

In this paper, we introduce the notions of ordered F -(F, h)-contraction and subcontraction in the setting of partial metric spaces. Some fixed point theorems for ordered F -(F, h)-contraction and subcontraction in 0-f -orbitally complete partial metric spaces are proved. Our results generalize some recent results of metric and partial metric spaces into the 0-f -orbitally complete partial metr...

Partial F tests play a central role in model selections in multiple linear regression models. This paper studies the partial F tests from the view point of simultaneous confidence bands. It first shows that there is a simultaneous confidence band associated naturally with a partial F test. This confidence band provides more information than the partial F test and the partial F test can be regar...

a modified f-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (nlpdes) is discussed. we use this method to construct many new solutions to the nonlinear whitham-broer-kaup system (1+1)-dimensional. the solutions obtained include jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

A partial function f on an k-element set Ek is a partial Sheffer function if every partial function on Ek is definable in terms of f . Since this holds if and only if f belongs to no maximal partial clone on Ek, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Ek. We show that for each k ≥ 2 there exists a unique minim...